Once you have found that you don’t need to use Game Center anymore, you can close your Game Center account as well as delete all contacts in the friend list and disassociate yourself from scores by following these steps:
1. First, to remove people from your Friends list, you can tap on their profiles and choose the Unfriend option.
2. Second, to deactivate your public profile, remove the email addresses, or change your nickname, you can go to Me > Account > View Account. Then here you can do the following:
- Disable your Public Profile.
- Remove Email from Account: this option will delete all emails from your email list.
- Choose another Nickname.
- Sign out of Game Center on all iOS devices.