Wyo. Stat. § 1-25-103
Except in a proceeding in which the court has issued a confidentiality order pursuant to W.S. 35-21-112 or any other court order allowing a party to maintain confidentiality of addresses, city or state of residence or other information identifying the residence of the party, public notice of the petition for a change of name shall be given in the same manner as service by publication upon nonresidents in civil actions. Upon good cause shown to the court or if the petitioners are petitioning to change a minor's name and are the minor's natural or adoptive parents or legal guardians and all natural or adoptive parents or legal guardians sign the petition, public notice shall not be required with respect to a petition for a change of name of a minor.
W.S. 1-25-103