Is there an OS that allows the same name for files in the same folder?
By "same name", I mean absolutely identical, including the extension.
VMS allows for identical file names in a directory. You can incorporate a 5 digit version number after identical names and extensions - so you have a great deal of latitude storing many, many, many identically named files on that OS/filesystem without needing to hack or modify it.
It's not clear how this will help you or what problem you are solving, but what you ask has been coded on production OS before.