Yes, beginning in 2022 the government of the Republic of Turkey asked people to use "Türkiye" in English rather than the traditional spelling, "Turkey," which dates back to the 18th century in English or possibly earlier. Yes, "Türkiye" is used in diplomatic contexts in English because that's what Turkey's government requests. However, it's hard to argue that it's a real English name given the orthography is obnoxiously foreign. There are two letters present that are not normally used in English orthography. The obvious one is Ü/ü, which is used here as a different vowel rather than the usual (but rare) usage in English to indicate that two vowels next to each other are NOT a diphthong. The less obvious but more troublesome letter is the dotted I, İ/i. It is ONLY used in English to write "Türkiye," inflicting the dotted/dotless I problem on anyone who writes "Türkiye" or "TÜRKİYE" regardless of the language.
There are tons of common words in English that use non English characters. No one argues those words need to be changed so I'm not sure why so many people here are so gungho about it.