I have an existing macro that first allows the user to open an xls
file, then it copies data from the selected file into the one where
the macro is located. This info is added to the existing data that's
already there. The user will run the macro multiple times (once for
each file to be added) ....thus ending with a "master" file composed
of data from each file they had selected.

That part is done. Now, on a separate sheet in the macro file I'd
like to create a log where each row shows the name of each file that
had been opened and copied into the master, along with the date when
this was done.

How would such a macro work?

Thanks.