JP Long wrote...
....
Cell A43 reads: =CONCATENATE('Contact Info'!B2," ",'Contact Info'!A2)
resulting in the cell populating with a name (i.e. Shelly Bell)

I want to determine how many times that specific name repeats in data found
elsewhere in the worksheet. These results will be displayed in C43; the
search is occurring C10:C38.

I have tried =COUNTIF (C10:C38, "A43") but xl looks for A43 as the text.
I have tried =COUNTIF(A43,C10:C38) the other way and the formula box shows
"Shelly Bell" as the results of A43; however, the results still come back as
zero (0).

Have you tried

=COUNTIF(C10:C38,A43)

?