Yes, if he is the one who fathered the child. Father's do not typically sign the birth certificate though, although he can be named on it.
no see links below
No - they simply list the names of the biological father and mother. A birth certificate does not prove the parents were married at the time the birth was registered.
see related link
The man on the birth certificate.
In Utah, if father isn't present at the birth of child, a paternity test has to be performed in order to list him on birth certificate.
Yes, if the father signs an acknowledgment of paternity.
I know that in the state of pennsylvania, the father must be present to sign the babies birth certificate in order for the baby to have the fathers last name.
Here in the Philippines, a mother can not just name any person as the father of her child in the Birth Certificate. They will look for a marriage contract as their reference when you named your child under his/her father's surname. Or if not married, they let the father fill up the Affidavit of Acknowledgement/Admission of Paternity at the back of the Birth Certificate.
I'm not absolutely sure if this applies to divorced couples, but I was born without my mother and father being married and they never got married. My birth certificate has my mother's last name.
yes
The mother must be of course. Yet, if the father can not be then no, or if you don't want the father to sign he does not have to. In Michigan when a child is born the mother fills out a form. The mother is asked if she is married and instructed based on her answer what information is needed. Paternity is established through court. If you are married or the father accepts paternity it is a legal matter. I'm still amazed at people stating the father signed the birth certificate. In Michigan there is no place on the certificate for any signature outside of the doctors.
The custodial parent can change the child's name to anything she wishes.