I have seen this on a advertisement. A teacher asks: "Who wants to do the problem 3?" And one of the students who is afraid that teacher would choose him to do the question try to hide his face, and tells himself:
"Please, don't be me, don't be me!"
I understand from the context that the student does not want to be the one whom the teacher would ask to do the question. So, he is avoiding the teacher and hopes that he would not be the one chosen.
But I wonder, is this "Don't be me" structure idiomatic, because this structure starting with "Don't ...." is generally used in imperatives. This sentences expresses a wish or a hope rather than a command.