No, there is no legal requirement to present an ID card simply to enter or travel within New Mexico as a U.S. citizen. Domestic travel between states does not mandate identification.
While not required for entry, carrying a valid government-issued photo ID (driver’s license, passport, state ID) is strongly recommended for:
If you’re driving, a valid driver’s license is required to operate a vehicle. International visitors should carry their passport and any required visa or ESTA documentation.