The Alabama Hills were named for the CSS Alabama, a Confederate warship deployed during the American Civil War. When news of the ship’s exploits reached prospectors in California sympathetic to the Confederates, they named many mining claims after the ship, and the name came to be applied to the entire range.
This comes from
Kyle, Douglas E. and Hoover, Mildred Brooke (1990). Historic Spots in California, p. 122. Stanford, California: Stanford University Press. ISBN0-8047-4483-1.