If I want to change my child's last name to mine how do I go about doing that? She was born out of wedlock and the man I was with claims she is not his. His name is on the birth certificate.

If his name is on the birth certificate, how did it get there? Did you just list him or did he voluntarily sign? While his name is on the because he's the legal father.

In either case, you will need to go to court to have the birth certificate changed. The legal father will have to agree to it.

But I think you have some deeper issues. You REALLY need to establish paternity.