Well, changing schools is a great time to get people to use your new name. If you decide to go for it, try to get to each class early so you can talk to the teacher and let him/her know what you'd rather be called. I knew a fellow who used to do that just to keep his rather embarrassing first name from being called on the first day of school.
BTW, I feel your pain regarding moving. I'm horribly shy as well, and my family moved regularly as I was growing up. I went to 10 different schools between Kindergarten and 11th grade, when I tested out.
