Query To Return Column Name And Date
I guessing that you need the examdate of the last exam that does not have a complete date?

Query

 SELECT fname,  
        CASE 
        WHEN exam1complete IS NULL THEN 'exam1date'
        WHEN exam2complete IS NULL THEN 'exam2date '
        ELSE 'exam3date' END AS columnname,
        CASE
        WHEN exam1complete IS NULL then exam1date 
        WHEN exam2complete IS NULL then exam2date 
        ELSE exam3date END AS examdate
FROM Information;


Result

fname   columnname  examdate
joe exam1date   2018-01-30
james   exam2date   2018-03-02
javier  exam3date   2018-04-01