McAlester is the county seat of Pittsburg County, Oklahoma. The population was 18,363 at the time of the 2010 census, a 3.4 percent iā¦McAlester is the county seat of Pittsburg County, Oklahoma. The population was 18,363 at the time of the 2010 census, a 3.4 percent increase from 17,783 at the 2000 census. The town gets its name from James Jackson McAlester, an early settler and businessman who later became lieutenant governor of Oklahoma. Known as "J. J.", McAlester married Rebecca Burney, the daughter of a full-blood Chickasaw family, which made him a citizen of the Chickasaw Nation.