I discovered that when you create your Game Center account, it will use the name on the credit card associated with your Apple ID.
Changing the name in Game Center application does not update your visible name for the other users. What sequence of steps is needed to get my new name displayed on devices that had friended me before I changed my display name?
Best Answer
Have you tried contacting your credit card provider?
Seriously, Apple's intention is that iOS Game Center friends are meant for "real" friends—rather than "Facebook friends"—so exposing your real name is not a threat. If you look at the issue this way, it feels more of a security enhancement than a threat. You can be sure the friend you are friending is actually the person you believe them to be.
Moreover, if you are underaged and can't attach your own credit card with your Apple ID, it is, in contrast, more secure to have the user's (kiddie's) name obfuscated.
Finally some legalese from the Game Center TOS:
For each friend's account you need to force an update, you should unfriend them and then establish the friend relationship again.