It is the word the Chinese would like non-Chinese to use when talking about the city. It’s a classic example of modern cultural re-appropriation, because Peking was the widely-accepted transliteration - until attitudes (and power) changed and the Chinese asked the world to use Beijing instead. It wouldn’t be particularly far-fetched to imagine Turks might also ask the world, eventually, to use their own spelling to refer to the country - especially considering the unfortunate overlap of the word “turkey” in English.