I agree with others that say it's ok but rather dull. I think it's a great element in a double-name though. It's like whipped cream that needs to be put on top of something.
I prefer
Clare, when it's on its own, but
Claire as part of a double name. Overall I much prefer
Clara. I love
Clara.
Lily-Claire would be pretty.
Clare Eleanor is very stately, I like that.