Caesar is speaking of himself in the third person in this quotation. To speak of yourself in the third person means to use your own name when referring to yourself, instead of saying "I."
If Caesar were speaking normally here, he would have said "Et tu, Brute?--"then I fall!"
To speak of himself in the third person adds a little more drama to the scene. Caesar is giving in to the idea that he is going to die, that he will cease to be. Now he is just about to become a historical figure, so it seems more fitting than it usually might to refer to himself this way.
Keep in mind also that Caesar is a title rather than a proper name. There were a number of Roman "Caesars." That makes it sound like he's saying something along the lines of, "You have killed your Caesar."