Murphy is a sailor from Carrigaloe Station that appears in the "Eumaeus" episode. Talking to Stephen, he claims to know (another) Simon Dedalus, and tells many tall tales of his travels around the world. Bloom suspects that much of what he says is made up or at least greatly embellished.
Murphy corresponds to the character Pseudoangelous from the Odyssey. In many ways, Murphy's tales make him sound more like Odysseus himself then Bloom does, but their falsity is meant to underlie the numerous fictions tied up in the idea of epic storytelling.