How did Billy end up on the HMS Bellipotent? What is the significance of the name "Bellipotent"? (Hint: what are the meanings of "bellicose" and "belligerent"?) In composing, Melville sometimes referred to this ship as the Indomitable. Why would he use either of these names for a war ship?

Billy Budd is press-ganged aboard the HMS Bellipotent. This was a common method of getting men to serve as sailors during the eighteenth century, when the story is set. Life onboard a ship was extremely harsh, so there was always a chronic shortage of men willing to serve in His Majesty's Navy.
That's where the practice of press-ganging came in. Men of suitable age would be rounded up and forced to serve aboard ships, especially during wartime, when the need for manpower was greatest. This is what happens to Billy Budd. England is threatened by Revolutionary France and needs all hands on deck to deter a potential invasion.
The name of Billy's ship is a reflection of the rapid drift to war. "Bellipotent" means "mighty in war." It comes from the Latin words bellum, meaning "war"—from where we also get the words "belligerent" and "bellicose"—and potestas, meaning "power." "Indomitable" would also have been an appropriate name for a ship about to go to war. "Indomitable" means "impossible to defeat."