What I really want to contribute here though is that your "we" from "what we call ourselves" doesn't include me. Like a lot of people outside the US, English is my native language and calling Americans Americans has always given me pause for thought. So I put it back to you:
Is it even possible for us to be wrong about what we call you?
In general, these kinds of errors come from historical limitations: orthography, linguistics, &c. At minimum, it’s respectful to try to adapt based on our better, contemporary understanding.
What? Peking wasn't a corruption at all. It accurately reflects the pronunciation encountered by... most Europeans who interacted with Chinese. Mandarin received official status in the 20th century.