There are files of the form

a-hire.txt, a-hire-1.txt,......, a-hire-9.txt, a-hire-rpt.txt

I would like to single copy command to copy them to files of the form
a-hire-0601.txt, a-hire-1-0601.txt,......, a-hire-9-0601.txt, a-hire-rpt-0601.txt .

I am just putting the month and day on the end of the file before the .txt.

copy a-hir*.txt a-hir*.0601.txt gives me a-hire.txt.0601.txt

That's clear why. You had a dot in the destination, that can't work.
The rename command puts after a dot the suffix of the file.
So instead of this:
copy a-hir*.txt a-hir*.0601.txt

use this:
copy a-hir*.txt a-hir*0601.txt

Just try that out.

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