If I didn’t create a user name for Game Center but I have a user name should I be concerned that someone has access to my account?

Hello micho85,

 Welcome to Apple Support Communities. We understand your concern with the Game Center account you didn't create, and we'd be happy to look into this with you.

In order to get better understanding of this situation, we'd like to gather some information:

• Did someone else create this account on your behalf?
• You've mentioned that you don't play games, does anyone else use your Game Center account to play games?

If you have an iOS device, go to: Settings > Game Center. Is it turned on?

If it is already on, are you signed in with your Apple ID?

For more information about Game Center, please check this out:

Use Game Center to play with friends

We'll be waiting for your response. Kind regards.