Washington is a town in McClain County, Oklahoma, United States. The population was 673 as of the 2020 census, a 0.2% increase from 2010. A post office called Washington has been in operation since 1904. The town was not named after George Washington, first President of the United States. The post office charter was granted May 10, 1904. According …Washington is a town in McClain County, Oklahoma, United States. The population was 673 as of the 2020 census, a 0.2% increase from 2010. A post office called Washington has been in operation since 1904. The town was not named after George Washington, first President of the United States. The post office charter was granted May 10, 1904. According to the Encyclopedia of Oklahoma History and Culture, the name was actually chosen to honor Caddo chief "Little Boy" George Washington, who had lived nearby.