048-4 Wyo. Code R. § 4-3
A new certificate of birth shall be prepared by the State Registrar of Vital Records for a child born in this state upon receipt of a certified copy of a court determination of paternity.
(a) The new certificate shall be on the form that was in use at the time of the birth, if possible.
(b) The surname of the child shall remain the same unless otherwise ordered by the court.
(c) The additional personal particulars required for the new certificate regarding the natural father shall be included if it is specified in the court order or in a notarized affidavit signed by the natural father.
(d) After preparation of the new certificate, the original certificate shall not be subject to inspection except upon order of a court of competent jurisdiction.
048-4 Wyo. Code R. § 4-3