With names in Column A, and dates in Column B, one way would be to enter a
name to count in C1, and the number of the month (Jan=1, Feb=2, ... etc.)
in
C2, and try something like this:

Another possibility which is more "visual" (you will be able to see the
matching rows). Assuming the same set up above, put this formula in D1...

=A1&" - "&MONTH(B1)

and copy down to the end of your data. Then put this formula in E1...

=IF(AND(A1=C$1,MONTH(B1)=C$2),COUNTIF(D$1:D$10000, "="&A1&" - "&C$2),"")

(using a number larger than the number of rows of data you have for the
10000 I used) and copy down to the end of your data (or beyond if your data
can grow). Now, when you put a name in C1 and a month number in C2, each
matching row will be flagged in column 'E' with the total number of hits for
that match.

Rick