If you have multiple names associated with a single UID, you have multiple names associated with that UID. But as far as the kernel is concerned, all thoser names are aliases for the SAME user.
That is, the name is a purely human fiction and the only thing ever stored is the UID.
For example's sake, say we have two lines in /etc/passwd:
user:50:50:...
resu:50:50:...
This defines two mappings from username to UID. Internally, only the numeric UID is used to determine who "someone is", so if resu
creates a file and sets the permissions to user:read/write, group:none, other:none, user
can still read it, because as far as the kernel are concerned, they are the same user.
/the/example/file
owner: 50
group: 50
permissions: rw-------
The only things stored in the file system, as far as ownership is concerned, is the numerical user ID and the numerical group ID. For mapping from numerical ID to human-friendly string, whatever is the first mapping found is the one used, because they're all identical.
In hort, don't give two users the same numerical ID, because if you do, you'e making life too hard on yourself.