A few minutes ago Apple sent out an email notification to inform users that they have updated Game Center terms & conditions to show full names associated with Apple IDs in friend requests.
We have changed the Game Center terms and conditions to provide you notice that if you send a friend invitation, the full name associated with your Apple ID will be shared with the recipient. If you accept a friend invitation, the full name associated with your Apple ID will be shared with the sender.
The change is already live in Game Center (you’ll have to sign in Game Center again and agree to the new rules), and can be tested right now by sending or receiving a friend request.
So why the real names? We assume Apple is looking for a way to make Game Center more “social” and to integrate Game Center’s userbase with iTunes Ping. You can’t search for a Game Center user on Ping basing on his nickname, but you can with a real name associated to an Apple ID.