Alvord is a town in Wise County, Texas, United States. The population was 1,334 at the 2010 census, an increase of 327 residents, or 32 percent growth, over the 2000 population.Originally known as Nina, Alvord adopted its present name in 1882 in honor of the president of the Fort Worth and Denver Railway. There is no connection with the Arizona bandit Burt Alvord. A post office was established in 1882. By 1890, Alvord was a retail center for area farmers.