Elissa is a girl’s name of English, Greek and Hebrew origin. Meaning in English: My God is bountiful;God of plenty. Meaning in Greek: From the Hebrew Elisheba, meaning either oath of God, or God is satisfaction. Meaning in Hebrew: From Elisheba, meaning either oath of God, or God is satisfaction. Elissa is a variant of Elizabeth and variant of Elisabeth. Famous bearer: Dido, Queen of Carthage, was known as Elissa. The name has 6 letters.