Wellman is a city in Terry County, Texas, United States. The city was formed in 1918 as a shipping point on the Santa Fe Railroad and na…Wellman is a city in Terry County, Texas, United States. The city was formed in 1918 as a shipping point on the Santa Fe Railroad and named after Augustus Ogden Wellman, who had been an assistant to the railroad's secretary and treasurer. Its population was 230 at the 2020 census.