I noticed they're still saying "Czeck republic" in English announcements in venues during the winter olympics, right now.It will take a while for the name change to catch on. I wonder whether it will survive a regime change, once Erdogan is gone.
Côte d'Ivoire is still often call Ivory Coast in English. In fact, Wikipedia still uses that name. I use "Czechia" at work but always have to explain it refers to the Czech Republic. There's also eSwatini, which previously ran under Swaziland.
Looking at it from another language, the bird/country pun doesn't happen in my native German, where it's Truthahn and Türkei.