Let's start with the simple facts before we get into all the swirling connotations. "Ulysses" is the Latin name for the Greek hero of Homer's epic, the Odyssey, on which Joyce's novel is based. As you read through the book and this guide, you'll learn that each of the eighteen sections in Joyce's book corresponds to a specific episode in Homer's. Why would Joyce do this? Well, there are a bunch of explanations for it, but we'll try to give the simplest and most straightforward of them. The Odyssey is the classic "epic poem." From the Western point of view, it marks the beginning of literature. By titling his novel, Ulysses, Joyce was harkening back to the start of literature and staking his place in it.
But he was also challenging Homer. With his novel, Joyce changed the way people thought of the concepts of "epic," and "hero." Instead of Ulysses experiencing adventures as he navigates his way home to Penelope, Joyce gives us an ordinary Jewish man by the name of Leopold Bloom, trying to make his way through a (relatively) normal day in Dublin, Ireland. By doing so, Joyce moves the genre of epic from wild globetrotting adventures into the mind of an average man. The Odyssey becomes a mental journey through the perils of everyday life: embarrassment, boredom, despair, lust, pride, etc. Making the journey a mental one allows Joyce to elevate the everyday to Homeric levels; he re-invents the epic by treating Leopold Bloom as a hero.
A last point to ponder: why did Joyce choose the Latin name, "Ulysses," over the Greek one, "Odysseus?" In actuality, Joyce first encountered Ulysses as a child and he happened to be exposed to the Latin name first. Thinking beyond that simple point the choice of "Ulysses" over "Odysseus" can raise some interesting questions.
In Homer's work, Odysseus is treated as a hero, renowned for his cunning and his sly intelligence. Yet in the first great Latin epic, the Aeneid, Virgil often refers to Ulysses as "the cruel Ulysses." It seems that Odysseus's deceitful tricks didn't correspond to Roman notions of honor. So then why choose the latter name, the one that is so often tied to an epithet? Does it simply sound better? Or is there some sort of turn-of-the-century equivalent to "Roman honor" in Dublin that Leopold Bloom does not meet?