Baby's initials!

I've always wanted to use either my mother's middle name (Ann) or my grandmothers first name (Alice) as a middle name for our daughter (due oct 4), however we've decided on a name that's starts with a C and our last name starts with a C...her initials would be CAC. Reading this I imagine years of torment, kids associating her initials with the word co*k...am I overthinking? Part of me thinks I'm just being crazy!