Let's begin with the obvious answer: Billy Budd is the name of the main character. Now let's try to go a bit deeper.
Who is Billy Budd? Late in the story, when Captain Vere is indistinctly heard murmuring Budd's name by his attendant, the attendant reports to the senior lieutenant, and the narrator notes that the lieutenant "too well knew, though here he kept the knowledge to himself, who Billy Budd was" (28.5). The way the narrator says it's as if the lieutenant is one of the few who really understood who Billy was and what happened to him. If we're keen readers, which we are, then we might ask ourselves: Do we know who Billy Budd really was?
Lieutenant Ratcliffe bemoans his loss and calls him a peacemaker. Captain Vere thinks he's a fine example of a man, and wants to promote him so that they can work together more closely. The men are inspired by him. Our narrator portrays him as completely natural, almost angelic. John Claggart, for reasons little understood, despises him. The chaplain is awed by his fearlessness in the face of death, his refusal to turn toward dogma or religion. The naval newspaper will later portray him as a treasonous man with murderous intent. A sailor's crude poem will turn him into a myth of the English sea fleet, a sentimental sea figure.
What do we think of him? As we skim over this list of different interpretations of Billy Budd, we can see that few of them portray him as human. All tend to either glorify him or demonize him; few leave him a man. Our narrator is no exception. He often goes so far as to compare Billy to Adam, to man before the Fall. The more closely we read Billy Budd, the more we realize that we don't actually know who Billy Budd is, that the man slips between the lines of the prose, and that he remains a mystery.
There are a bunch of ways to read Billy Budd. One is as a morality tale. Another is as a historical document of what life in the English fleet was like after the Nore Mutiny. Recently, the legal vagaries of Billy's case have made it a novel that gets studied and discussed in law schools. All of these are valid ways to read the book, but our title declares right from the start that it is fundamentally a human story. Our main question, even if it is an unanswerable one, is: Who is Billy Budd?