Billy Pilgrim's last name is an allusion to John Bunyan's Pilgrim's Progress but also refers, more universally, to Billy's role as a pilgrim, a person on a spiritual journey. Billy is an optometrist, a symbol of his role as one who sees. He enters the army as an assistant chaplain and at first has a conventionalized Christianity that most of the soldiers reject. After he is shattered by witnessing the bombing and utter destruction of Dresden, he eventually does go on a journey, kidnapped by the alien Tralfamadorians, who bring him to their planet. This leads him to a spiritual transformation. The Tralfamadorians show him that the past, present, and future are all one, strung out like a mountain range, so Billy learns to live in the present, to not fear death, and to adopt the phrase "so it goes" to signal his acceptance that life is what it is.
His first name, Billy, is a very common, everyday name, but Vonnegut is ever the jokester, so the name possibly refers to slang for speed, an amphetamine that might send one on a "trip," something completely appropriate to the counter-cultural drug culture of 1969, the year of the book's publication, and to Billy's interplanetary journey.
Ilium has a double meaning. Ilium really is a city in New York, home to the Rensselear Polytechnic Institute. Since the novel explores the role of technology, good and bad, it is not surprising that Vonnegut placed his protagonist, who witnessed the destructive effects of technology on Dresden, in a city housing a technical institute. Ilium is also the Trojan city completely destroyed by the Greeks, another reference to the destruction of Dresden and to the human capacity for violence.