Thats right. Eithne and Aine are the same name, pronounced the same way, but spelled differently, as I also explained above. Enya is a merely her handler's attempts to anglicize the spelling to make it appear to English speakers in such a way as they might have a stab at actually pronouncing it correctly. This matters a great deal for things like air play on radio. You don't want pronounciation of the name to be an impediment to the music getting played, and to create name recognition.