Is it normal and/or expected?
Doesn't this mess up the "@" mentions? (or would it mess it up once the new user decides to register?)
The Display Name has no real meaning to the system: you can set it to whatever you want (within reason), by design. The site identifies you by your user number (9740 for the new person, 394 for the Terry we all know), which is unique to each site (e.g. I'm user 64 here, and 32986 on Server Fault).
This won't generally affect @ mentions unless both users happen to be participating on the same question or chat room (which is possible, but not a big enough problem to warrant requiring a unique display name: you can figure out who they're referring to by context).