According to Jewish tradition, Azura is the twin sister of the Biblical Abel, and becomes the wife of Seth/Chet, her youngest brother, since Abel died. Cain also had a twin sister that became his wife, Awan.
I generally don't like names with a 'z' or a stressed 'z' sound, but I think this is a really cool and pretty name. I'm not happy about it being Biblical, so I wouldn't use it myself, but as long as it doesn't catch on, it sounds cool, even if quite foreign. Instead of the Bible, this track reminds me of a track by 808 State titled Azura. I don't like it much, though. It's the memories I like.
Azura is the name of a Daedric Princess (like a goddess) in the Elder Scrolls video game series. She is the lady of dawn and dusk, and maintains the domain of Moonshadow, a twilight realm of shades and half-thoughts.
I like this spelling more than "Azure", but I still feel weird about naming my kid after a color. I like "Skye" more than "Sky", and "Azura" more than "Azure". If I would ever name my kid after a color (tough chance), I would probably add a letter or something to 'modernize' it.