From Halopedia, the Halo wiki
The Odyssey was sent to Epsilon Eridani, where it would settle the world that would become Reach. The launching of the Odyssey sparked the first wave of human expansion beyond the confines of the Sol system.
The name 'Odyssey' derives from an epic poem written by the Greek poet, Homer. The story follows a commander, Odysseus, who gets lost on his return from the Trojan War, sailing to various places over the course of two decades. The name is fitting for the ship because of the parallels: humanity embarks on a long voyage after emerging from the Interplanetary War.
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