I'm going to be absolutely honest here: I think that is a wonderfully creative idea for a family set! This is just a suggestion; how about using
Keshet as the family surname? The word "keshet" actually means "rainbow" in Hebrew, I believe.
Of your list, I like
Rory,
Flavia,
Esmeralda, and
Azure; the other names, I don't care much for. For "orange," may I suggest
Sienna?
Indigo isn't really my style, so I can't say that I enjoy it; though, it's the only name I can find (meaning
Indigo). For a twin sister, how about
Ianthe, since it also means "violet" (and starts with the letter "I")?