Holcomb HAW-kəm is a city in Dunklin County, Missouri, United States. The population was 635 at the 2010 census. A post office called Holc…Holcomb HAW-kəm is a city in Dunklin County, Missouri, United States. The population was 635 at the 2010 census. A post office called Holcomb has been in operation since 1882. The community has the name of Lewis Holcomb, a county sheriff.