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(5) If, within the first year after the child's date of birth, the parents cannot mutually agree on a surname, either one can submit a signed, sworn statement that acknowledges the disagreement, states the father was not available within the time allowed by law for filing of the birth certificate to participate in the choice of his child's surname, and requesting that the name be changed to the father's surname, in which case the father's surname shall be entered on the amended birth certificate as the surname of the child.
(b) (1) If the mother was not married at the time of either conception or birth or between conception and birth, the name of the father shall not be entered on the certificate of birth and all information pertaining to the father shall be omitted, and the surname of the child shall be that of either:
(A) The surname of the mother;
(B) The mother's maiden surname; or
(C) Any combination of the surnames listed in subdivisions (b)(1)(A) and (b)(1)(B).
(2) (A) If an original, sworn acknowledgment signed by both the mother and the biological father of a child, on a form provided by the state registrar or the department of human services, is submitted to the office of vital records at any time prior to the child's nineteenth birthday, the legal surname of the father may be entered on the certificate as that of the child, and the father's name and other personal information may be entered in the spaces provided on the birth certificate, notwithstanding the absence of a marriage relationship between the parents of the child.
(B) The acknowledgment form shall be in the form of an affidavit, shall contain the social security numbers of the mother and father of the child and shall be approved by the state registrar and the department of human services. The state registrar and the department of human services shall modify the form to comply with the minimum regulations for the form, which are finalized by the secretary of health and human services. An acknowledgment executed in conformity with this section shall be valid as long as it is executed on a form approved by the state registrar and the department of human services. A voluntary acknowledgment of paternity may be completed by a minor, if a parent or legal guardian of the minor is present and consents at the time of completion of the acknowledgment.