If you (the mother) and your baby's father are from a country other than the United States and are not married: you both must have current United States IDs. If both of you do not have IDs, the father will not be listed on the birth certificate. The baby will be given the mother's last name.f you (the mother) and your baby's father are from a country other than the United States and are not married: you both must have current United States IDs. If both of you do not have IDs, the father will not be listed on the birth certificate. The baby will be given the mother's last name.