@kancer,
This is the Facebook Real Names Policy in action. Get used to it.
Your only recourse is to prove you are either using a legit stage name (as in Lady Gaga) or you are in danger of being abused/stalked due to the use of your real name.
You have neither. You are not going to win this.
Legit game companies on Facebook (think Zynga) don't push users to make tons of friends in order to gain an in-game benefit. So talk to Zynga or whoever makes the game, and make your case to them about transferring rights. Be prepared to show proof that it's your account (most likely from being able to respond to an email sent to the email account used to set up the second FB account. Even if you can't get into FB anymore, that does not affect an independent email provider).