N.M. Stat. § 62-11-1
Any party to any proceeding before the commission may file a notice of appeal in the supreme court asking for a review of the commission's final orders. If an application for rehearing has been filed, a notice of appeal must be filed within thirty days after the application for rehearing has been refused or deemed refused because of the commission's failure to act within the time specified in Section 62-10-16 NMSA 1978. If an application for rehearing has not been filed, a notice of appeal must be filed within thirty days after the entry of the commission's final order. Every notice of appeal shall name the commission as appellee and shall identify the order from which the appeal is taken. Any person whose rights may be directly affected by the appeal may appear and become a party, or the supreme court may, upon proper notice, order any person to be joined as a party.
NMS § 62-11-1