N.M. Stat. § 53-17-14
A foreign corporation authorized to transact business in this state shall procure an amended certificate of authority in the event it changes its corporate name or desires to pursue in this state other or additional purposes than those set forth in its prior application for a certificate of authority by making application therefor to the commission [secretary of state]. The requirements in respect to the form and contents of the application, the manner of its execution, the filing of an original and a copy, which may be a photocopy of the original after it was signed or a photocopy that is conformed to the original, with the commission [secretary of state], the issuance of an amended certificate of authority and the effect thereof shall be the same as in the case of an original application for a certificate of authority.
NMS § 53-17-14