N.M. Stat. § 53-19-50
Name.
A foreign limited liability company may register with the commission [secretary of
state] under any name, whether or not it is the name under which it is registered in the
state or other jurisdiction of organization, as long as the name could be registered by a
domestic limited liability company pursuant to Section 3 [53-19-3 NMSA 1978] of the
Limited Liability Company Act.