We roll along with so many weird changes in characters. What if the Mandarin changed nothing at all but his name? The idea here would be to give him a name that doesn't invoke China at all. After all, aside from his origin, does China really figure all that much into what he does? This alone could be the reason he changes his name. He thinks globally and wants to self-identify globally.
I did a quick Wikipedia check and apparently there is no Marvel character named "Monarch." (There are three DC characters with that name.) So for purposes of this thread, we'll imagine the Mandarin rebranding himself as "Monarch."
With that change in place, all Marvel would have to do is stop referencing his birth parents or childhood home town. Simply say his parents died and he was raised by an old woman in a remote village. Don't even say "in Asia." Just say "a remote village." After all, who really cares? He's not trying to be China's top dog. If we're being honest, he wants to rule the universe. He wants to be God. He thinks he rightfully should be and one day surely shall. (Of course the universe he ruled would be Hell for all but the very strongest and most vicious.)
Draw his face like Johnny Depp with goatee and mustache. Let him look like Cardinal Rilieu, the villain of the Three Musketeers novel. With muscles.
So Marvel does a story arc where the Mandarin announces his rebranding as Monarch. By the end of the arc, a whole lot of people (victims, captives) are calling him Monarch. Tony would probably resist but by the end of the arc he gives up, because he wants to communicate with all these people who only know this villain as Monarch.
Next time the character shows up he is simply Monarch, no mention ever again of having had another name.
Ten years from now, maybe Monarch could be a movie villain and even be popular in China!