It's beautiful! I think it needs a very elegant, though that need not mean too established or everyday, middle name. Nothing too fussy. I like the look of something like
Caoimhe Rose or
Caoimhe May or
Caoimhe Anne, but cannot decide whether the middle names are boring place-holders, or emphasise the beauty of
Caoimhe.
On the side...I knew a lovely woman named
Caoimhe. She was forever telling people how to say and spell her name, three, four times, which she found a nightmare, but people always said she had a lovely name when they got their heads around it. She was very classy, elegant, witty, very Irish, dark-haired, grey-eyed, tall and drop dead lovely. Only
Caoimhe I've ever known, and one who creates a very positive image of the name.