I go by my middle name, Clare. I have for nearly 5 years now, and haven't had a problem. Some family friends and friends had some trouble adjusting at first, and some family still accidentally call me my first name, or nickname, but I don't mind. If you start calling them their middle name at a young age, it won't be a problem at all...at school they'd just simply tell the teacher they go by 'such-and-such'. I had a friend who went by her middle name, when we were in grade school and younger..and have a fellow highschool classmate go by her middle name. It's quite common. Now, of course I use my actual first name for important papers related to state standardized testing, job applications, and my driver's license, but other than that!
HTH