The town name is the same as that of the oldest known name for a cottage (est. 1667) in the area. The cottage's name also contains the word "Morgongåva" (Translated: "Wedding gift" or "Morning gift"). The reason why the cottage was called so is not entirely clear, but according to some, the name choice came about due to a love triangle. During the 17th century, the Patron of Molnebo, just outside Morgongåva, had an affair with one of his maids. She became pregnant and the Patron was afraid that his wife would find out about the relationship. He "bought" one of his farmhands who would provide for the maid and her future child. Once the maid servant and the farmhand were married, they received a cottage as a wedding gift, or a "morning gift", hence the name. Quote from Heby Municipality: "Morgongåva is the extension of the name of a recent two-croft called so. The origin of the name is claimed to be a bride gift from a lord of the manor to one of his maids. "