The name Davina is a Hebrew baby name. In Hebrew the meaning of the name Davina is: Cherished. American Meaning: The name Davina is an American baby name.In American the meaning of the name Davina is: Cherished.eminine of David. Scottish Meaning: The name Davina is a Scottish baby name. In Scottish the meaning of the name Davina is: Beloved or friend. Feminine form of David.Feminine form of David: Beloved or friend, adopted from the Hebrew.