new facebook account and game center

Hello ,

Thank you for reaching out to Apple Support Communities.

If you go to Settings > Game Center > Sign Out, you can sign out of your current account. You can then sign in using these steps:

"On your iPhone or iPad

1. Open Settings. Scroll to Game Center, then tap it.
2. If Game Center isn’t on, turn it on, then sign in with your Apple ID.*
3. Tap the Nickname field to enter a name that your friends will see when you play games together. If you can’t think of a name, you can choose one of the randomly generated suggestions.
4. To personalize the picture that shows with your nickname, tap Edit in the circle at the top of the page. From here, you can create a Memoji, use an existing one, or customize how your nickname's initials appear."

More details can be found here: Use Game Center to play with friends

You can leave feedback regarding FaceBook with Game Center by going to iCloud

Cheers!