The last suggestion by RagDyer is probably your problem, where
you are formula view. The Ctrl+` (accent grave) toggles between
formulas and nonformulas and is the same as
Tools, Options, View (tab), uncheck/check Formulas
You want it to be unchecked.

If you still have a problem after making sure that the column(s) are
formatted as General and not as Text, the next step would be to
make sure that you did not place a space
before the equal sign. A single quote at the beginning would mess up
a formula as it is a means of indicating a text cell..

The correct terminology is concatenation not grouping
=A1 & " " & B1 first then lastname
=B2 & ", " & A1 lastname comma space firstname

Not the problem you describe but there are similarities, if you used
the fill handle and you see the same results (same name) going down
as opposed to the formulas that you see,
it means that you have calculation turned off (or the wrong formula).
A quick indication of calculation being turned off is if
F2+Enter works. The solution for that would be to turn
Calculation to automatic.
Tools, Options, Calculation (tab), Calculation: turn on automatic
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HTH,
David McRitchie, Microsoft MVP - Excel [site changed Nov. 2001]
My Excel Pages: http://www.mvps.org/dmcritchie/excel/excel.htm
Search Page: http://www.mvps.org/dmcritchie/excel/search.htm