Dougherty is a town in Murray County, Oklahoma, United States. The population was 199 as of the 2020 Census. The community was first known as Henderson Flat. On September 3, 1887, a post office was established here and called Dougherty, Indian Territory. The post office took its new name from banker William Dougherty of Gainesville, Tex…Dougherty is a town in Murray County, Oklahoma, United States. The population was 199 as of the 2020 Census. The community was first known as Henderson Flat. On September 3, 1887, a post office was established here and called Dougherty, Indian Territory. The post office took its new name from banker William Dougherty of Gainesville, Texas.