Chiara is a lovely and romantic Italian name that's familiar but not widely used here: a real winner. You might consider Chiara instead of Claire, Clara, Cara, or even Keira.
Santa Chiara, Aglicized as St. Clare, was a follower of Saint Francis of Assisi.
Two members of European cinema royalty, Catherine Deneuve and Marcello Mastroianni, named their now grown daughter Chiara.
Chiara currently ranks Number 8 in Italy, and is also well used in Switzerland, Germany and Austria.