The American Heritage English Dictionary says: Middle English, from Old French azur, from Medieval Latin azura, from Arabic al-lâzaward, the Azure : al-, the + lâzaward, Azure (from Persian lâjward, lapis lazuli). [noted -ed]
I think this name sounds so unique but not outlandish. It reminds me of a beautiful yet quirky girl who loves art or music. Would name my daughter this if I ever had one.
I slightly prefer the sound of Azura, but this is the one that isn't used in the Bible, even if it derives from that name. This is a cool and pretty name, but it sounds quite foreign. I like the meaning behind it, though, as I love the sky, and blue in its many shades is my favorite color. I'm not sure what name this could go with, though.
I once saw this movie names "Azur et Asmar" or "The Princes' Quest" in English-speaking countries (the original is "Azur et Asmar" and is a French movie.) I much prefer it as a boy's name when spelled without the "e".
I really like this name, but I would never name my daughter this, because it's like naming a kid "Orange" or "Green" or "Purple" or something. At least it's not as bad as naming your kid "Blue". :)