Original: Dissatisfied with his stage name as Davy (and Davie) Jones, which in the mid-1960s invited confusion with Davy Jones of The Monkees, Bowie re-named himself after the 19th century American frontiersman Jim Bowie and the knife he had popularized.
Simplified: He uses the alias David Bowie because David Jones sounded too much like Davy Jones (of The Monkees). He took the name Bowie from Jim Bowie, who invented the Bowie knife.