Usually, when both parents agree who the father is, they will agree on a last
name and give the child that last name on the birth certificate (and it does not
have to be the same as the father or the mother). This is easiest to do at the
hospital when the child is born but can be done later if both parents agree. If
both parents do not agree, the one who wants the change can petition the New
York State Supreme Court asking the court to change the child’s last name and
saying why this would be in the best interests of the child. This can be initiated
by the unmarried father once legal paternity has been established. You should
talk to a lawyer about this procedure.