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.
What does Rose mean?
IS a bloom word: directly the English flower name, from Latin 'rosa' (the rose). Also used historically as a short form of Germanic names with the element 'hrod' (fame), but the enduring modern sense is the flower itself.