There are multiple origins and meanings for the name Azalia:
1. Bashkir (Азалия) and Tatar (Turkic) name, derived from the Persian (ازلی) [azali] meaning - "eternal, everlasting, prevenient; infinite; unchanging; constant". See Azaliya
2. Comes from the ancient Greek word (ἀζαλέος) [azaléos] meaning - "dry, dried". Azalea - Latin name of a flower that thrives in sandy soil.