Hi ScootergirlATX,
Welcome to the Support Communities!
The Game Center profile is tied to your Apple ID. Does your husband have his own Apple ID account? If not, he can create one, then sign out of Game Center and sign in with his own account.
Here are some articles that may help:
Using Game Center
http://support.apple.com/kb/ht4314
Using your Apple ID for Apple services
http://support.apple.com/kb/HT4895
The "Frequently Asked Questions" section of this article may be relevant for you.
Apple ID: What to do after you change your Apple ID
http://support.apple.com/kb/HT5796?viewlocale=en_US&locale=en_US
Cheers,
- Judy