A bohemian is named after a place its namesakes never came from. The word rests on two mistakes, one about geography and one about lifestyle.
The first mistake was medieval. From the 15th century, the French called Roma travelers bohémiens, people from Bohemia. The name had nothing to do with the Czech people who actually lived there. Etymonline says the belief that the Roma originated there was wrong. They may simply have reached Western Europe by way of Bohemia. They may also have been confused with Hussite heretics, who were being driven out of Bohemia around the same time.
English made a parallel error. Gypsy, recorded around 1600, is a worn-down form of "Egyptian," reflecting a link to Egypt that was presumed rather than confirmed.
The second shift happened in Paris. By 1834 bohémien also described artists and writers who lived like wanderers, poor, unconventional and indifferent to respectable society. Henri Murger's stories of this world, gathered as Scenes of Bohemian Life, made the type famous in the 1840s. Puccini's 1896 opera La Bohème was based on them.
The artist sense reached English in 1848, in William Makepeace Thackeray's novel Vanity Fair. In 1862 the Westminster Review defined a bohemian as an artist or writer who "secedes from conventionality in life and in art." By 1861 English could also use "Bohemia" for an artists' quarter, wherever it was.
The idea crossed the Atlantic quickly. In San Francisco, Bret Harte wrote as "The Bohemian" for The Golden Era from 1861. In 1872 local journalists and artists founded the Bohemian Club.
The real Bohemia has its own naming story. Its Latin name, Boiohaemum, joins the Boii, a Celtic people who once lived there, with a Germanic word meaning "home." The Boii were pushed out by Germanic tribes in the early 1st century. So the word carries, at its root, the home of a people who had already left, applied to a people who never lived there.