I have no idea how much he is bothered by it, but he explicitly said eight years ago that he wanted to be referred to as "Andrew Cole". I found a vaguely amusing article from the time about what the possible implications of such a name change (and look out for the Jonathan Woodgate fact).
Also, did you know that he had a brief assault on the pop charts? Or had you forgotten? Let me remind you (he was still "Andy" Cole then, obviously):