The ten gallon hat was not actually worn by true cowboys, since the sheer size of it would have made the wearer a sitting duck for a dirty rotten scoundrel. Bowlers were more common, as was a style dubbed the Boss of the Plains: a wide-brimmed model made by Stetson.

As for the name, it most likely comes from the Spanish word, galon. This was a braided hatband worn by Mexican cowboys (vaqueros), and the larger variations were tall enough to fit ten of these bands (ten galon hat). 

Pragmatism aside, the hat eventually gained widespread attention after actors began wearing them in Wild West films beginning in the 1920s. They just look cooler. Let's face it, no one is going to take you seriously as a lawman in a bowler hat.