If looking at the word Exodus from a religious perspective, keep in mind that the Exodus in the bible was a direct result of the plagues God sent to force the pharaoh's hand, culminating with the deaths of the first born. It all ended with God directly intervening by killing pharaoh and his army by crushing them in the sea, and allowing the Israelites to escape.
One could say the black goo/spores and various forms of neo/xeno represent the plagues. Either the embryos onboard Covenant, or David's other counterparts which were no doubt taken offline due to people's concerns represent the firstborn. The paradise engineers or the colonists represent the Israelites, and pharaoh is David. Seeking to enslave and destroy supposedly inferior forms of life out of anger and a sense of superiority, only to anger and be crushed by the gods, which would fit in with Ridley's engineers discovering David's evil and coming after him.
Plus I just thought it sounded like a good name for a ship and a movie.
