I tend to think about user uploads as just another kind of user data, and so it all goes into a database. Obviously, make sure the database you are going to use for this is a good choice for that, for example, a SQL database isn't necessarily right.
If it makes sense, I try to use a url pattern that makes sense in the context of the usage pattern of the site, for example:
example.com/username/users_file.jpg
If there's just no obvious way to do that, and I have to use a surrogate key, I just live with it:
example.com/files/abc123
example.com/files/abc123/
example.com/files/abc123/users_file.jpg
All three are the same file. in particular, the abc123
is all that the app needs to look up the file, the extra bit at the end is there so that browsers get a good hint at what the file should be named when it's saved to disk.
Doing it this way means that no matter what the original file is named, it always is unique to the user. Even if the user wishes to upload 100 files with the same name, all are unique.