Though I haven't seen IRON MAN 3 yet, I recently responded to an online comment on the general theme of "why did the adaptors bother to use the name of the Mandarin if they weren't going to keep anything else about the character?" As usual, though I'm aware of some of the immediate contingent circumstances (e.g., Chinese investors and audiences), my response takes a more generalizing approach.
Though I can't claim to have any direct knowledge of Hollywood thinking, I'm
going to say that this is not a phenomenon not confined to comic-book
adaptations. I think a lot of Hollywood adaptors have or come to have an
adversarial relationship with the material adapted. In both the films KISS ME
DEADLY and MODESTY BLAISE, the adaptors use assorted bits from the novels
adapted, but play with those bits to suit their desires, often to pursue themes
opposed to the original authors. That's why Frank Miller's SPIRIT doesn't
resemble Eisner's SPIRIT. Miller didn't want to make a respectful Eisner movie;
he wanted to make a Frank Miller movie.
Why even keep those bits if
they're going to change them entirely? I think the adaptors are under some
pressure to have SOMETHING that resembles the property the company buys. I have
no idea who in the chain of command said, "Let's use the Mandarin in IM3," but
once it was sent down, the adaptors were stuck with it. In this case the
exigencies of political correctness probably informed the changes in the
character, rather than personal preference as it seems to have been with DEADLY
and BLAISE. But the principle is the same.