When I was a kid, I went through a phase of calling myself Diana, followed by a phase of calling myself Julie. When I finally got back to my real name, I was so relieved! Carol is right for me.
But I love the name Claire for myself, too... or I did, until I got to know a woman with that name who turned out to be awfully small of mind. No more Claire.
Liked Catherine, too, until my brother married one and she turned out to be Evil Incarnate.
I do like Wren, though -- I knew someone once who was given Wren as a nickname for Catherine (-rine, Wren), and I think that's lovely.
But if I really had to choose... I'd be Pearl, the name I gave my little Pearlygirl kitty.