Bogard is a city in Carroll County, Missouri, United States. The population was 167 at the 2020 census. Bogard was originally known as Bogard…Bogard is a city in Carroll County, Missouri, United States. The population was 167 at the 2020 census. Bogard was originally known as Bogard's Mound, after a tumulus near the site which a pioneer citizen named Bogard used as an observation tower. The village plat was made in 1884. A post office called Bogard Mound was established in 1872, and the name was changed to Bogard in 1884.