Odysseus's boat did not have an individual nickname. It is now referred to as a Homeric ship or galley. In the epic "Odyssey" by Homer, Odysseus loses all of his ships while travelling home to Ithaca, then builds a new ship on the island of Calypso.
The detailed account of Odysseus building a ship on Calypso's island reveals many insights into the shape and materials of Homeric galleys. Odysseus fells 20 trees and crafts and joints a broad floor, yard-arms, gunwales, a mast, rudder and sails. The goddess Calypso brings him various trimmings to build the ship, including adzes, augurs and cloth for the sails.