That is a question to ask your advisor. There are most likely rules on how the dissertation has to look like, including things like where to put the university and institute, how to mention the advisor and, of course, also how and where to put your name (e.g. "name must be the same as on transcript/certificate").
If there happen to be no rules regarding that at your specific university, then your advisor might still be the best to ask, as he knows both the names A,B and also the field you are aiming to work in, so he can say which name might be better.
edit: This recent question here might be relevant to you: Proving authorship when name in publications does not match name in passport