1. Open your device's 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.

For more reference, please refer to this Apple link: 

Use Game Center to play with friends