In English, name Eliza means – My God is bountiful. God of plenty. A diminutive of Elizabeth frequently used as an independent name. Famous bearer: Eliza Doolittle, the Cockney heroine of George Bernard Shaws play Pygmalion, from which the musical My Fair Lady was derived.. Other origins for name Eliza include – English, Israeli, Hebrew, French. Name Eliza is most often used as a girl name or female name.