Punctuating questions containing questions [duplicate]
This is a matter of style, so consult your style guide, either the one you've adopted or the one thrust upon you. I prefer The Chicago Manual of Style, which, in its 16th edition recommends that when two question marks collide, only one remains in the text. Section 6.120 has the following examples:
Who starred opposite Richard Burton in Who’s Afraid of Virginia Woolf?
Who wrote “Are You a Doctor?”
Where were you when you asked, “Why so blue?”