I've known two women named Shahrazad, both from Pakistan. It's definitely one of my favorite Arabic / Persian names, though if I were to ever use it I'd probably go with Scheherazade, since I feel like it's less "foreign" in the Western World.
I have to admit, considering what a clever woman and great storyteller Shahrazad was, her name's meaning disappoints me. "Person of the city"? Come on! There are a million other ways to spell it, though: Sheherezade, Sharazade, Shaherazad, and my personal favorite, Scheherezade.