Okla. Stat. tit. 10, § 557.20

Upon the birth of a child contemplated by a validated gestational agreement, the intended parents under such validated gestational agreement shall be listed as the parents on the child's certificate of birth that is to be filed with the state registrar of vital statistics as provided by Oklahoma law, and neither the gestational carrier nor any spouse of the gestational carrier if she is married shall be listed on said certificate of birth.