There is a known bug with the "give stamped files a new name" functionality. If the new name expression makes reference to the file name, or any metadata field, it will always use the data from the first file, from the batch being stamped, resulting in all the new names being equal.
As workaround you may add a counter to the new name expression, to make it variable.
It's already fixed here and will be included in the next release.
If you want to test the beta 3.4.1, contact me from your license registered email address.