rename
renaming would be bad, because i often look for player in searching their name.
And about the feature, i doubt that the result would be good, because i expect a lot of Homer Simpsons in the game(and i am sure that players will also play for offending names like hitler which will be extra work when the proposal is declined), maybe some dudes also get their real name player into their roster which could be cool but it won't be special anymore.
Maybe the GM could add names to the database when people create their account, they already had to check them when you register and when you use a normal name their you could be lucky that he get drafted some day.