Hey gregary240,
Under Settings > Game Center, does it show your Apple ID? Or where do you see this unknown account?
If you feel someone has gained access to your account, we'd recommend changing your Apple ID password using one of the methods outlined here:
As to your device, is it jailbroken? If not, it is difficult to install any software on your device without your knowledge or the device not being in your possession. That said, check for a configuration profile in Settings and if you find one that you don't recognize as from a job, school, etc, delete it.
"Delete the app and its configuration profile
To delete an app and its configuration profile, follow these steps.
- Delete the app
- Touch and hold the app until it jiggles.
- Then tap the delete button in the upper-left corner of the app to delete it. If you see a message that says, "Deleting this app will also delete its data," tap Delete.
- If the app has a configuration profile, delete it.
- Go to Settings > General > Profiles or Profiles & Device Management,* then tap the app’s configuration profile.
- Then tap Delete Profile. If asked, enter your device passcode, then tap Delete.
Restart your iPhone, iPad, or iPod touch."
Cheers!