Azura is a name that is very unique, and stands out. I think it's beautiful, and comes from "Azul" and "Azure" which both mean blue.
Asami is a Japanese name that means "morning beauty" and is also beautiful.
I'm a bit undecided on the middle name. Rose is beautiful and traditional, but Lily is equally as beautiful and not as common as rose but still quite common. I think a common middle name coupled with such a unique first name creates a lovely contrast.
I am more inclined to go with Lily as it works better in Japan (translates to Riri, Rose translates to Rozu) and I am moving to Japan in a couple of years.
So, which name?
Azura Rose
Asami Rose
Azura Lily
Asami Lily
Any other suggestions or comments are welcomed!