There are 2 US Post Offices in Luna County serving a total of 25,095 residents equating to 12,548 residents per post office. It's estimated that approximately 40,054 packages are handled across the 2 county post offices annually. Luna County is a county located in the U.S. state of New Mexico. As of the 2010 census, the population was 25,095. Its county seat is Deming. This county abuts the Mexican border. Luna County comprises the Deming, NM Micropolitan Statistical Area."