Now, despite the fact that Melville just spent three chapters telling us about how tense things are after the mutiny, everybody's pretty calm and chilled out on Billy's ship.
Here, we're introduced to the Captain of the ship, Edward Fairfax Vere. He's a forty-year-old bachelor, and a very well respected man, and is known to be mindful of the men on board his ship.
On top of all this, Vere is also a totally nice, modest, and down to earth guy. Occasionally, he's a bit dreamy, standing at the prow of the ship and gazing out at the stars and such, but in general he's got it together and everybody likes him.
He does have this nickname, though, which is "Starry Vere" (6.4). It comes from a buddy of his, Lord Denton, who pulled it from a poem by Andrew Marvell, and ever since the name has stuck.