Refactoring Series of UNIONs in single table (SQL/SYBASE)
If you subtract 1 from FieldNum and divide the result by 3 using integral division, you will get the following results for FieldNum values of 1 till 6:

FieldNum | (FieldNum - 1) / 3
---------+-------------------
    1    |         0
    2    |         0
    3    |         0
    4    |         1
    5    |         1
    6    |         1


And if you replace / with % (the modulo operator), the results will be like below:

FieldNum | (FieldNum - 1) % 3
---------+-------------------
    1    |         0
    2    |         1
    3    |         2
    4    |         0
    5    |         1
    6    |         2


Now, in case the idea isn't yet clear, the (FieldNum - 1) / 3 expression can be used as a grouping criterion in addition to EntityID (for some reason called EntityNum in your query). And the results of (FieldNum - 1) % 3 could be used to determine particular rows (would-be columns) within the subgroups defined by (FieldNum - 1) / 3.

Finally, if my attempts at verbal description hasn't really succeeded, here's a query that uses the above two expressions to produce the results you are after:

SELECT
  EntityID,
  MAX(CASE (FieldNum - 1) % 3 WHEN 0 THEN Memotext END) AS Date,
  MAX(CASE (FieldNum - 1) % 3 WHEN 1 THEN Memotext END) AS Name1,
  MAX(CASE (FieldNum - 1) % 3 WHEN 2 THEN Memotext END) AS Name2
FROM EQ
WHERE FieldNum BETWEEN 1 AND 6
GROUP BY
  EntityID,
  (FieldNum - 1) / 3
;


And here you can find a "live" SQL Fiddle demonstration. To be honest, the demo uses SQL Server to run the query, but I would expect Sybase to produce the same results. (I'm assuming that FieldNum is an integer-typed column and that Sybase, like SQL Server, automatically applies integral division when both operands of / are integers.)