Fizzbuzz in COBOL, Verbose dinosaur style
As I'm sure you are aware, COBOL tends to be written one way at one site, another way at another.

Often things like name prefixes, and paragraph/SECTION prefixes cannot be other than dictated. Same with case of identifiers.

I dislike WSnn- (drives people nuts trying to insert numbers so that new data can be located rationally rather than in the order of arrival in specification) and WS- (similar for the LINKAGE SECTION) but am happy with W-/L-/LS- (or nothing). Absolutely hate single-word identifiers. Even these days with forewarning of what may appear later, it is plain dumb to have them there waiting for some compiler-change to make them invalid.

Also, since COBOL has no concept of "main", it is something to avoid pretending exists.

For paragraphs, or SECTIONS, I go with two numerics. Then with each subsequent level, append an alpha, A, D, G, J, M etc (allowing for insertions), and keep all related paragraphs/SECTIONS together, physically. Your program only has one level, so it doesn't really matter what you do in that one.

Nicely laid-out. I tend to be more extreme, but the effort you've invested impresses the reader (if they are a programmer, rather than a 9-5-er). 

Hate the comments. 

I'd remove all the redundant code (you don't need an ENVIRONMENT DIVISION, for instance). 

Ah, for these last two, they have been generated for you, so I'd suggest copying an existing model program rather than using the OpenCOBOLIDE bolierplate.

I only use VARYING with things that, well, vary. So I'd use TIMES. Describe the situation better. You have to do more typing, but in addition to the better description of the data, your code will be faster than using VARYING.

Forget ideas like using REM. COBOL has done remainders since day one, a considerable time ago, so why (I don't know the answer to this) is there a function for it? In Enterprise COBOL (IBM Mainframe) REM would return a floating-point item, then converted to what you define in your program. Wow, do we need that?

I would work on the data-names a bit, but they are better than VAR1, VAR2 (or WS13-VAR1 and WS34-VAR2).

Here's an example of how I like to format a program:

http://ibmmainframes.com/viewtopic.php?p=278927#278927

And since that is a link, here's the code:

   IDENTIFICATION DIVISION.
   PROGRAM-ID. BBHEXD.
   ENVIRONMENT DIVISION.
   DATA DIVISION.
   WORKING-STORAGE SECTION.
   01  W-WHEN-COMPILED                      PIC X(8)BX(8).

   01  W-DISPLAY-HEX-MAX-UIND      USAGE IS INDEX.
   01  W-FIRST-TIME-FLAG                    PIC X VALUE "Y".
       88  W-FIRST-TIME-IN-PROGRAM          VALUE "Y".
       88  W-NOT-FIRST-TIME-FLAG            VALUE "N".

   01  W-WORK-BYTE-FOR-CALC         COMP    PIC S9(4) VALUE ZERO.
   01  FILLER REDEFINES W-WORK-BYTE-FOR-CALC.
       05  FILLER                           PIC X.
       05  W-WORK-BYTE                      PIC X.

   01  W-LEFT-HALF-BYTE-NUM         COMP    PIC S9(4).
   01  W-RIGHT-HALF-BYTE-NUM        COMP    PIC S9(4).
   01  W-BYTES-TO-OUTPUT            COMP    PIC S9(4).
   01  W-BYTES-MOVED                COMP    PIC S9(4).

   01  W-HEX-ALPHA-SUB              COMP    PIC S9(4).
   01  W-HEX-ALPHA-TABLE VALUE "ABCDEF".
       05  FILLER OCCURS 6 TIMES
            INDEXED BY W-HEX-ALPHA-IDX.
           10  W-HEX-ALPHA                  PIC X.

   01  W-DISPLAY-HEX.
       05  W-LEFT-HEX                       PIC X.
       05  W-RIGHT-HEX                      PIC X.

   01  W-HEX-TO-DISPLAY-LEFT-TABLE VALUE SPACE.
       05  FILLER OCCURS 1 TO 132 TIMES
           DEPENDING ON W-BYTES-TO-OUTPUT
           INDEXED BY W-DISPLAY-HEX-LEFT-IND.
           10  W-HEX-TO-DISPLAY-LEFT        PIC X.
               88  W-HEX-TO-DISPLAY-LEFT-IS-EMPTY
                                            VALUE SPACE.
   01  W-HEX-TO-DISPLAY-RIGHT-TABLE VALUE SPACE.
       05  FILLER OCCURS 1 TO 132 TIMES
           DEPENDING ON W-BYTES-TO-OUTPUT
           INDEXED BY W-DISPLAY-HEX-RIGHT-IND.
           10  W-HEX-TO-DISPLAY-RIGHT       PIC X.

   01  W-BYTE-TO-DISPLAY-TABLE VALUE SPACE.
       05  FILLER OCCURS 1 TO 132 TIMES
           DEPENDING ON W-BYTES-TO-OUTPUT
           INDEXED BY W-DISPLAY-BYTE-IND.
           10  W-BYTE-TO-DISPLAY            PIC X.
   01  W-CONVERT-TO-HEX-FROM-DIGIT   COMP   PIC S9(4).

   01  W-CONVERTED-HEX-DIGIT                PIC X.
   01  W-CONVERTED-HEX-DIGIT-NUM
         REDEFINES W-CONVERTED-HEX-DIGIT    PIC 9.

   01  W-CONVERTED-HEX-DIGIT-NUM4           PIC 9(4).
   01  FILLER REDEFINES W-CONVERTED-HEX-DIGIT-NUM4.
       05  FILLER                           PIC XXX.
       05  W-CONVERTED-HEX-DIGIT-NUM4L      PIC 9.

   01  W-COLS-LINE.
       05  FILLER OCCURS 1 TO 132 TIMES
           DEPENDING ON W-BYTES-TO-OUTPUT.
           10  FILLER                       PIC X.

   01  W-COLS-TABLE.
       05  FILLER                           PIC X(10) VALUE
           "----+----1".
       05  FILLER                           PIC X(10) VALUE
           "----+----2".
       05  FILLER                           PIC X(10) VALUE
           "----+----3".
       05  FILLER                           PIC X(10) VALUE
           "----+----4".
       05  FILLER                           PIC X(10) VALUE
           "----+----5".
       05  FILLER                           PIC X(10) VALUE
           "----+----6".
       05  FILLER                           PIC X(10) VALUE
           "----+----7".
       05  FILLER                           PIC X(10) VALUE
           "----+----8".
       05  FILLER                           PIC X(10) VALUE
           "----+----9".
       05  FILLER                           PIC X(10) VALUE
           "----+----0".
       05  FILLER                           PIC X(10) VALUE
           "----+----1".
       05  FILLER                           PIC X(10) VALUE
           "----+----2".
       05  FILLER                           PIC X(10) VALUE
           "----+----3".
       05  FILLER                           PIC X(02) VALUE
           "--".

   LINKAGE SECTION.

   01  L-DATA-LENGTH COMP PIC S9(8).

   01  L-BBHEXD-CONTROL-BLOCK.
       05  L-BBHEXD-CB-MAX-LINE         COMP PIC S9(4) VALUE +80.
           88  L-BBHEXD-CB-MAX-LINE-VALID    VALUE +80 +132.
       05  L-BBHEXD-CB-CHUNK-LENGTH     COMP PIC S9(4) VALUE ZERO.
           88  L-BBHEXD-CB-CHUNK-LENGTH-ZERO VALUE ZERO.
       05  FILLER                            PIC X(96) VALUE SPACE.

   01  L-DATA-PICX1-FOR-USING PIC X.

   01  L-DATA-TO-DISPLAY REDEFINES L-DATA-PICX1-FOR-USING.
       05  FILLER OCCURS 99999999 TIMES
             INDEXED BY L-DTD-BYTE-FOR-C-AND-C-IDX.
           10  L-DTD-BYTE-FOR-CONV-AND-COPY PIC X.


   PROCEDURE DIVISION USING
                                    L-DATA-PICX1-FOR-USING
                                    L-DATA-LENGTH
                                    L-BBHEXD-CONTROL-BLOCK
                                    .
   00-CONTROL SECTION.

       PERFORM                      10-FIRST-TIME
       PERFORM                      30-CNV-LK-DATA-TO-HEX-AND-DISP
       GOBACK
       .
   10-FIRST-TIME SECTION.

       IF W-FIRST-TIME-IN-PROGRAM
           PERFORM                  10A-SAY-WHO-WE-ARE
           SET W-NOT-FIRST-TIME-FLAG
                                    TO TRUE
       END-IF

       PERFORM                      10D-CHECK-OUTPUT-LENGTH
       PERFORM                      10G-SET-OUTPUT-LNGTH-AND-CHUNK
       .
   10A-SAY-WHO-WE-ARE SECTION.

       MOVE WHEN-COMPILED           TO W-WHEN-COMPILED
       DISPLAY "BBHEXD This program compiled on "
                                    W-WHEN-COMPILED
       .
   10D-CHECK-OUTPUT-LENGTH SECTION.

       IF ( NOT L-BBHEXD-CB-MAX-LINE-VALID )
           DISPLAY "BBHEXD maximum line length should be 80 or 132"
           DISPLAY "BBHEXD found&gt;" L-BBHEXD-CB-MAX-LINE "&lt;"
           CALL "FOODUMP"
       END-IF
       .
   10G-SET-OUTPUT-LNGTH-AND-CHUNK SECTION.

       IF L-BBHEXD-CB-CHUNK-LENGTH-ZERO
           MOVE L-BBHEXD-CB-MAX-LINE
                                    TO W-BYTES-TO-OUTPUT
       ELSE
           IF ( L-BBHEXD-CB-CHUNK-LENGTH
               GREATER THAN L-BBHEXD-CB-MAX-LINE )
               DISPLAY "BBHEXD Sorry, chunks ignored, too big"
               DISPLAY "BBHEXD Chunks&gt;" L-BBHEXD-CB-CHUNK-LENGTH "&lt;"
               DISPLAY "BBHEXD Maxlen&gt;" L-BBHEXD-CB-MAX-LINE "&lt;"
               MOVE L-BBHEXD-CB-MAX-LINE
                                    TO W-BYTES-TO-OUTPUT
           ELSE
               MOVE L-BBHEXD-CB-CHUNK-LENGTH
                                    TO W-BYTES-TO-OUTPUT
           END-IF
       END-IF

       SET W-DISPLAY-BYTE-IND       TO W-BYTES-TO-OUTPUT
       SET W-DISPLAY-HEX-MAX-UIND   TO W-DISPLAY-BYTE-IND

       IF L-DATA-LENGTH EQUAL TO ZERO
           DISPLAY "BBHEXD You want to display zero bytes?"
           DISPLAY "BBHEXD Do not expect to see them"
       END-IF
       .
   30-CNV-LK-DATA-TO-HEX-AND-DISP SECTION.

       SET W-DISPLAY-HEX-LEFT-IND
           W-DISPLAY-HEX-RIGHT-IND   
           W-DISPLAY-BYTE-IND       TO +1
       MOVE ZERO                    TO W-BYTES-MOVED

       PERFORM                      30A-BYTE-BY-BYTE-CONVERT
         VARYING                    L-DTD-BYTE-FOR-C-AND-C-IDX
         FROM                       1
         BY                         1
         UNTIL                      L-DTD-BYTE-FOR-C-AND-C-IDX
           GREATER THAN             L-DATA-LENGTH

       IF ( W-BYTES-MOVED NOT EQUAL TO ZERO )
           MOVE W-BYTES-MOVED       TO W-BYTES-TO-OUTPUT
           PERFORM                  99A-DISPLAY-PART-OF-OUTPUT
       END-IF

       .
   30A-BYTE-BY-BYTE-CONVERT SECTION.

       MOVE L-DTD-BYTE-FOR-CONV-AND-COPY
             ( L-DTD-BYTE-FOR-C-AND-C-IDX )
                                    TO W-WORK-BYTE

       DIVIDE W-WORK-BYTE-FOR-CALC  BY 16
         GIVING                     W-LEFT-HALF-BYTE-NUM
         REMAINDER                  W-RIGHT-HALF-BYTE-NUM

       MOVE W-LEFT-HALF-BYTE-NUM    TO W-CONVERT-TO-HEX-FROM-DIGIT
       PERFORM                      30AA-CONVERT-HALF-BYTE
       MOVE W-CONVERTED-HEX-DIGIT   TO W-LEFT-HEX
       MOVE W-RIGHT-HALF-BYTE-NUM   TO W-CONVERT-TO-HEX-FROM-DIGIT
       PERFORM                      30AA-CONVERT-HALF-BYTE
       MOVE W-CONVERTED-HEX-DIGIT   TO W-RIGHT-HEX

       IF ( W-DISPLAY-HEX-LEFT-IND
           GREATER THAN W-DISPLAY-HEX-MAX-UIND )
           PERFORM                  99A-DISPLAY-PART-OF-OUTPUT
           SET W-DISPLAY-HEX-LEFT-IND
               W-DISPLAY-HEX-RIGHT-IND
               W-DISPLAY-BYTE-IND
                                    TO +1
       END-IF

       MOVE W-LEFT-HEX              TO W-HEX-TO-DISPLAY-LEFT
                                        ( W-DISPLAY-HEX-LEFT-IND )
       MOVE W-RIGHT-HEX             TO W-HEX-TO-DISPLAY-RIGHT
                                        ( W-DISPLAY-HEX-RIGHT-IND )
       MOVE W-WORK-BYTE             TO W-BYTE-TO-DISPLAY
                                        ( W-DISPLAY-BYTE-IND )
       ADD +1                       TO W-BYTES-MOVED
       SET W-DISPLAY-HEX-LEFT-IND
           W-DISPLAY-HEX-RIGHT-IND
           W-DISPLAY-BYTE-IND       UP BY +1
       .
   30AA-CONVERT-HALF-BYTE SECTION.

       IF ( W-CONVERT-TO-HEX-FROM-DIGIT GREATER THAN 9 )
           SUBTRACT 9               FROM W-CONVERT-TO-HEX-FROM-DIGIT
             GIVING                 W-HEX-ALPHA-SUB     
           SET W-HEX-ALPHA-IDX      TO W-HEX-ALPHA-SUB
           MOVE W-HEX-ALPHA ( W-HEX-ALPHA-IDX )
                                    TO W-CONVERTED-HEX-DIGIT
       ELSE
           MOVE W-CONVERT-TO-HEX-FROM-DIGIT
                                    TO W-CONVERTED-HEX-DIGIT-NUM4
           MOVE W-CONVERTED-HEX-DIGIT-NUM4L
                                    TO W-CONVERTED-HEX-DIGIT-NUM
       END-IF

       .
   99A-DISPLAY-PART-OF-OUTPUT SECTION.

       MOVE W-COLS-TABLE            TO W-COLS-LINE
       DISPLAY                      W-COLS-LINE

       DISPLAY                      W-BYTE-TO-DISPLAY-TABLE
       DISPLAY                      W-HEX-TO-DISPLAY-LEFT-TABLE
       DISPLAY                      W-HEX-TO-DISPLAY-RIGHT-TABLE
       MOVE SPACE                   TO W-BYTE-TO-DISPLAY-TABLE
                                       W-HEX-TO-DISPLAY-LEFT-TABLE
                                       W-HEX-TO-DISPLAY-RIGHT-TABLE
       MOVE ZERO                    TO W-BYTES-MOVED

       . 


To demonstrate the usefulness of meaningful names, here's a version with the names rubbished:

   IDENTIFICATION DIVISION.
   PROGRAM-ID. UGLY.
   ENVIRONMENT DIVISION.
   DATA DIVISION.
   WORKING-STORAGE SECTION.
   01  W-A                      PIC X(8)BX(8).

   01  W-B            USAGE IS INDEX.
   01  W-C          USAGE IS INDEX.

   01  W-D              PIC S9(9).
   01  FILLER REDEFINES W-D.
       05  FILLER                           PIC X(5).
       05  W-E         PIC 9(4).
   01  W-F PIC X VALUE "Y".
       88  W-F-Y VALUE "Y".
       88  W-F-N VALUE "N".

   01  W-G         COMP    PIC S9(4) VALUE ZERO.
   01  FILLER REDEFINES W-G.
       05  FILLER                           PIC X.
       05  W-H                      PIC X.

   01  W-I         COMP    PIC S9(4).
   01  W-J        COMP    PIC S9(4).
   01  W-K            COMP    PIC S9(4).

   01  W-L              COMP    PIC S9(4).
   01  W-M VALUE "ABCDEF".
       05  FILLER OCCURS 6 TIMES
            INDEXED BY I.
           10  W-N                  PIC X.

   01  W-O.
       05  W-P                       PIC X.
       05  W-Q                      PIC X.

   01  W-R.
       05  FILLER OCCURS 1 TO 132 TIMES
           DEPENDING ON W-K
           INDEXED BY J.
           10  W-S        PIC X.
               88  W-S-Y
                                            VALUE SPACE.
   01  W-T.
       05  FILLER OCCURS 1 TO 132 TIMES
           DEPENDING ON W-K
           INDEXED BY K.
           10  W-U       PIC X.

   01  W-V.
       05  FILLER OCCURS 1 TO 132 TIMES
           DEPENDING ON W-K
           INDEXED BY L.
           10  W-W            PIC X.
   01  W-X   COMP   PIC S9(4).

   01  W-Y                PIC X.
   01  W-Z
         REDEFINES W-Y    PIC 9.

   01  W-AA           PIC 9(4).
   01  FILLER REDEFINES W-AA.
       05  FILLER                           PIC XXX.
       05  W-AB      PIC 9.

   01  W-AC.
       05  FILLER OCCURS 1 TO 132 TIMES
           DEPENDING ON W-K.
           10  FILLER                       PIC X.

   01  W-AD.
       05  FILLER                           PIC X(10) VALUE
           "----+----1".
       05  FILLER                           PIC X(10) VALUE
           "----+----2".
       05  FILLER                           PIC X(10) VALUE
           "----+----3".
       05  FILLER                           PIC X(10) VALUE
           "----+----4".
       05  FILLER                           PIC X(10) VALUE
           "----+----5".
       05  FILLER                           PIC X(10) VALUE
           "----+----6".
       05  FILLER                           PIC X(10) VALUE
           "----+----7".
       05  FILLER                           PIC X(10) VALUE
           "----+----8".
       05  FILLER                           PIC X(10) VALUE
           "----+----9".
       05  FILLER                           PIC X(10) VALUE
           "----+----0".
       05  FILLER                           PIC X(10) VALUE
           "----+----1".
       05  FILLER                           PIC X(10) VALUE
           "----+----2".
       05  FILLER                           PIC X(10) VALUE
           "----+----3".
       05  FILLER                           PIC X(02) VALUE
           "--".

   LINKAGE SECTION.

   01  L-A PIC X.

   01  L-B REDEFINES L-A.
       05  FILLER OCCURS 99999999 TIMES
             INDEXED BY M.
           10  L-C PIC X.

   01  L-D COMP PIC S9(8).

   01  L-E.
       05  L-F         COMP PIC S9(4) VALUE +80.
           88  L-F-VALID    VALUE +80 +132.
       05  L-G     COMP PIC S9(4) VALUE ZERO.
           88  L-G-Y VALUE ZERO.
       05  FILLER                            PIC X(96) VALUE SPACE.


   PROCEDURE DIVISION USING         L-A
                                    L-D
                                    L-E
                                    .
   00-A SECTION.
       IF W-F-Y
           MOVE WHEN-COMPILED       TO W-A
           DISPLAY                  "UGLY program compiled on "
                                    W-A
           SET W-F-N                TO TRUE
       END-IF

       IF ( NOT L-F-VALID )
           DISPLAY "UGLY maximum line length should be 80 or 132"
           DISPLAY "UGLY found&gt;" L-F "&lt;"
           CALL "FOODUMP"
       END-IF
       IF L-G-Y
           MOVE L-F                 TO W-K
       ELSE
           IF ( L-G
               GREATER THAN L-F )
               DISPLAY "UGLY Sorry, chunks ignored, too big"
               DISPLAY "UGLY Chunks&gt;" L-G "&lt;"
               DISPLAY "UGLY Maxlen&gt;" L-F "&lt;"
               MOVE L-F             TO W-K
           ELSE
               MOVE L-G             TO W-K
           END-IF
       END-IF   
       SET L                        TO W-K
       SET W-B                      TO L
       SET J
           K   
           L                       TO ZERO

       PERFORM                      00-B
         VARYING                    M
         FROM                       1
         BY                         1
         UNTIL                      M
           GREATER THAN             L-D


       IF ( NOT W-S-Y )
           SET W-C                  TO J
           MOVE W-C                 TO W-D
           MOVE W-E                 TO W-K
           PERFORM                  00-D
       END-IF

       GOBACK
       .
   00-B SECTION.

       MOVE L-C
             ( M )
                                    TO W-H

       DIVIDE W-G                   BY 16
         GIVING                     W-I
         REMAINDER                  W-J

       MOVE W-I                     TO W-X
       PERFORM                      00-C
       MOVE W-Y                     TO W-P
       MOVE W-J                     TO W-X
       PERFORM                      00-C
       MOVE W-Y                     TO W-Q

       SET J
           K
           L                        UP BY +1

       IF ( J GREATER THAN W-B )
           PERFORM                  00-D
           MOVE SPACE               TO W-R
                                       W-U
           SET J
               K
               L
                                    TO +1
       END-IF

       MOVE W-P                     TO W-S
                                        ( J )
       MOVE W-Q                     TO W-U
                                        ( K )
       MOVE W-H                     TO W-W
                                        ( L )
       .
   00-C SECTION.

       IF ( W-X GREATER THAN 9 )
           SUBTRACT 9               FROM W-X
             GIVING                 W-L     
           SET I                    TO W-L
           MOVE W-N ( I )           TO W-Y
       ELSE
           MOVE W-X                 TO W-AA
           MOVE W-AB                TO W-Z
       END-IF

       .
   00-D SECTION.

       MOVE W-AD                    TO W-AC
       DISPLAY                      W-AC

       DISPLAY                      W-V
       DISPLAY                      W-R
       DISPLAY                      W-T
       . 


Now, there are a couple of bugs in this version. Enjoy finding them, as you first have to work out, with no aid, what the program does.

Since you have GnuCOBOL, track down the discussion area at SourceForge.Net, the current home of GnuCOBOL.