Legal Question in Family Law in New Mexico

32A-4-4. Complaints; referral; preliminary inquiry. (2005)

Statute text

A. Reports alleging neglect or abuse shall be referred to the department, which shall conduct an investigation to determine the best interests of the child with regard to any action to be taken. The name and information regarding the person making the report shall not be disclosed absent the consent of the informant or a court order.

The statute above says they can't disclose your name without your consent or a court order, but it provides no remedy. If you file a complaint with the police department (assuming it was the police who disclosed your name) they may discipline the cop. If it was the CYFD worker who disclosed your name I understand they have a complaint process; it's hard to locate but you might try their constituent affairs office: http://cyfd.org/about-cyfd/constituent-affairs. (CYFD doesn't take criticism well).