Clarice is nice, but I've always wanted to say it like "cla-rice", so I prefer the spelling
Clarisse.
It's very classy and under appreciated IMO.
I've never seen Silence of the lambs (and I don't intend to either!) but the two
Clarice's (and
Clarisse's) I've known didn't get much hassle from it, so I wouldn't let it bother you too much.