Remove part of file name from many files

I use file history to backup my files. Thus I found out that it appends the time backuped to the end of file name.
But the recording software that I use doesn't allow the input file name to be longer than 15 characters.
So, I would like to know on how to batch rename the files as most of the files have the same time stamp. Renaming around 1500 files one by one is very tedious.