I pronounce it like you, but then in my dialect the body part is a CLIToris, not a CLYtoris, so I don't have that problem.
I like Clytie Camilla, Clytie Miranda, Clytie Rosamond and Clytie Rowena.
What about Clytie Christiana? Clytie Annabel? Clytie Philippa? Clytie Gertrude?