What about something like "I strongly feel that this name better suits my identity," or something along those lines? It's pretty much the same thing a lot of people say when they change their names legally.
I am registered as [Birth Name] in your [Class] class on [Days] from [time] to [time]. I am sending this message to let you know that I prefer to go by a shortened version of my name, "[Name]." I strongly feel that [Name] better suits my identity, so please use that name when you address me.
It's good to mention the new name twice, and do it so that the prof unequivocally understands which name is to be used. Every once in a while, you'll get someone who is so busy that he or she will misread the message, check the roster, and say, "Well, I've already got that name on my roster. Problem solved." We can get pretty busy right before the start of term.
What do you think?