N.M. Stat. § 62-15-4
The name of each cooperative shall include the words "electric" and "cooperative" and the abbreviation "inc."; provided that limitation shall not apply if, in an affidavit made by the president or vice president of a cooperative and filed with the secretary of state, it appears that the cooperative desires to transact business in another state and is precluded therefrom by reason of its name. The name of a cooperative shall distinguish it from the name of any other corporation organized under the laws of, or authorized to transact business in, this state. The words "electric" and "cooperative" shall not both be used in the name of any corporation organized under the laws of, or authorized to transact business in, this state, except a cooperative or a corporation transacting business in this state pursuant to the provisions of the Rural Electric Cooperative Act.
NMS § 62-15-4