What does Luna mean?
Luna is the Latin word for 'moon' and the name of the Roman goddess who personified it, counterpart to the Greek Selene. The meaning is literal and well established.
What does Diana mean?
Diana is the Roman goddess of the hunt, later identified with the moon (counterpart to Greek Artemis/Selene). Her name most likely derives from a root meaning 'heavenly, divine' rather than 'moon' itself, so the lunar sense is through the goddess's identification, not literal etymology.