N.M. Stat. § 60-13-13.2
Licensees; identical or similar names.
The division shall not accept an application, shall not issue a license and shall
require a change in the name of a proposed license if the proposed name is identical to
or in the opinion of the director so similar that it may cause confusion with a name on a
pending application or an existing license. Any person aggrieved by the decision of the
director may appeal the decision to the commission.