The Apple Game Center application that connects iOS games to a global scoreboard and has other social elements has changed their terms of service. The ToS was modified to allow Apple to push your real name through Game Center. Above is a screenshot of what it looks like.
Your real name is only being pushed in the form of friend requests. So if you value your privacy, avoid sending friend requests to people on Game Center. Below is an excerpt from the new ToS:
IMPORTANT NOTE: 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.