I like Connor and Caoimhe because they sound well together, but I agree with spelling the latter name differently. Her teachers will hate you!
(And she will hate having to correct everyone.)
We have three girls and my husband and I always battled over the name game. I hate names that can be shortened with a "Y' ending. Like Rebecca to Becky, Jessica to Jessie, etc. My name is Jennifer and I HATE being called Jenny. My husband won the battle with our second and chose Caitlyn. I spelled it weird hoping to prevent people from calling her Kate or Katie, but they still do. Makes the hair on the back of my neck stand up.
Oops, sorry, I got a little carried away...