Odysseus has a grown son he's never met: Telemachus. Homer begins his story with Telemachus's perspective, and so does Joyce.
But Joyce puts a difficult twist on this parallel by recycling his autobiographical self-portrait from his earlier works: Stephen Dedalus.
WHO: Stephen Dedalus
Bloom and Stephen are unrelated but vaguely aware of each other (Bloom is an acquaintance of Stephen's father).
Book One of Ulysses, called the Telemachia, includes the first three episodes, before Bloom is even introduced, focusing on Stephen suffering the absence of any spiritual father and the abstract threat to his spiritual mother from unspiritual 'suitors'.
(Book Two comprises 12 episodes centered on Bloom called the Odyssey, Book Three is 3 final episodes with both characters, called the Nostos.)