It’s not possible to have two files of the same name in the same location, however it sounds more like you mean that you want users to be able to overwrite each other’s files. If that is the case, then you need to modify the permissions on the folder granting users the Modify permission, and also make certain that you propagate the permissions down through existing files and/or subfolders. Really all the users would need is Change permission to make them overwrite other user’s (or tehir own) files.
You can set these permissions on a per-user basis, or you can create an Active Directory security group for the purpose.
To prevent users from loosing data you might want to consider using Shadow Copies. What this will do is take a copy of the file every X hours and keep a specific number of copies so that you can look at the older versions. If the files are uploaded more often that the snapshots are taken then you will miss versions.