Martin is a home rule-class city in Floyd County, Kentucky, in the United States. The population was 634 as of the 2010 census. Martin develo…Martin is a home rule-class city in Floyd County, Kentucky, in the United States. The population was 634 as of the 2010 census. Martin developed as a coal mining community in the early 1900s. Its first post office, established in 1910, was named "Bucks Branch" after a tributary of Beaver Creek, the stream that runs through the city. In 1913, the community was renamed "Smalley" after a local landowner, Smalley Crisp. By 1915, however, the community had been renamed "Martin" after the postmaster, Martin Van Allen. The post office began officially using this name in 1926.