(1) Except as otherwise provided by law, the name of the spouse at the time of conception or, if none, the spouse at birth must be registered as the other parent of the child. The surname of the child must be registered as designated by the child's parents.

    (2) Except as otherwise provided by law, if the child's mother was not married at the time of conception or birth, the name of the other parent must not be entered on the certificate of birth without the written consent of the mother and without the completion, and filing with the state registrar, of an acknowledgment of parentage by the mother and the individual to be named as the other parent. The acknowledgment of parentage must be completed in the manner provided in the acknowledgment of parentage act. For a certificate of birth completed under this subsection and on the written request of both parents, the surname of the child must be designated by the child's parents.

    (3) If the name of the child's other parent cannot be shown under subsection (1) or (2), the child must be given the surname designated by the mother.

    (4) If the parentage of a child is determined by a court of competent jurisdiction, the name of a parent must be entered on the certificate of birth as found and ordered by the court. The surname of the child must be entered on the certificate of birth as designated by the child's mother.

    (5) If the child's other parent is not named on the birth registration, no other information about the other parent may be entered on the registration.

    (6) After May 30, 1979, a birth certificate must not contain a reference to the legitimacy or illegitimacy of a child.