Our default at Silver Bulletin is AP style, so it's "Turkey," not "Türkiye". But I think AP is right in this case; it's a big ask to request that your official name in another language requires a special character.
This whole Türkiye thing is ridiculous, like forcing us to call Spain España or Germany Deutschland. It's weird that the BBC's broadcasting arm is going with it, while the website is sticking with Turkey, like other written publications seem to be. We don't have umlauts here.