Is it better to just legally change my name?

Well, I wouldn't change your name until at least 24, or around that age. I don't know how old you are so.... because any younger and you really don't know a few years from now if you're going to regret changing your name. So you should just introduce yourself as your preferred nickname. I know, because I've seriously considered changing my own name, but I decided not to because of all the people it would let down, and I knew I wasn't old enough yet to comprehend if that's what I really wanted.