N.M. Admin. Code § 11.21.2.35
A petition for amendment of certification may be filed at any time by an exclusive representative or an employer to reflect such a change as a change in the name of the exclusive representative or of the employer, or a change in the affiliation of the labor organization. The director shall dismiss such a petition within thirty (30) days of its filing if the director determines that it raises a question concerning representation and the petitioner may proceed otherwise under these rules. If the director finds sufficient facts to show that the amendment should be made, after giving all parties notice and an opportunity to submit their views, the director shall issue an amendment of certification within thirty (30) days of the filing of the petition. The director's decision dismissing the petition or issuance of amended certification may be appealed to the board pursuant to the procedures set out in Section 22, above.
N.M. Admin. Code § 11.21.2.35