I can see some issues would be that:

a. No one would recognize their friends anymore. I wonder if that could be remedied by putting a field into the profile/search info that says "Formerly known as..." So anyone who searches you up will recognize your old name if they knew you before.
b. People would just change their names on the fly. Maybe if a limit on the number of name changes can be implemented (like 3, for example) and you can't ever revert back to your old name, meaning once you decide to give it up, it's gone forever.

Would these ideas bounce?