Please note that I am not licensed in your state and this answer is for informational purposes only.
Find the family court in your county. Go to the family court clerk in person and ask what the procedure is. The clerk should be able to provide you with the information you are looking for.
Best of luck.
I do not practice in New Mexico, so I can only give you general information. It seems to me that you are asking two things: 1) Can your husband adopt your daughter, and 2) Can you change your daughter's last name. For the change of name, you probably can do that on your own. However, I would recommend that you do the step-parent adoption as your husband is really your daughter's father. During the course of the adoption you can change her last name. In order to have your husband adopt your daughter, you must either get her biological father's consent, or have a court waive his consent to the adoption. If the biological father has not developed a relationship with your daughter and has not supported her financially, a court will almost certainly grant the adoption. You don't say how long your husband has been raising your daughter, but if it has been for over a year, and her biological father has not been involved, you should be able to obtain the step-parent adoption. I strongly recommend that you work with an experienced adoption attorney, who you can find through the American Academy of Adoption Attorneys. Best of luck.