Lighthouse in Cozumel Cozumel owes its name to the Mayan Indians who populated the island, according to Mayan legend, Cozumel was the home of the goddess Ixchel, goddess of love and fertility. The inhabitants of the area built religious temples dedicated to this goddess and as a sign of gratitude she sent her favorite bird, the swallow. Since then the Mayans named the island "The land of swallows."