What are you talking about? It’s
Turcja, of course!

Don’t confuse official names with common speech, and don’t confuse the country with the state.
For over a century the official name is
Türkiye or, in full version,
Republic of Türkiye. This is the name of the state and it’s how it should appear in official documents. Similar to how the state I’m citizen of is called
Rzeczpospolita Polska, how the committee deciding how state officials should name things decided that Kaliningrad is now
Królewiec, or how Trump decreed that Gulf of Mexico is now
Gulf of America if referred to by people falling under the government regulation. The government of Türkiye also decided that when the name is used in English, its short name should stay
Türkiye, whereas e.g. Poland decided it should be
Poland (instead of native
Polska).
Independent of that, recently United Nations corrected their use of the name to
Türkiye (instead of
Turkey), and Turkish(!) government promotes that name abroad. But neither Türkiye, nor anybody else ever changed how the common speech refers to either the country or the state. And while — as all nationalists — they also insist on using the same word for the country, and for the same reason it became popular trait among some Turkish people, this is not the norm. So far it’s still Turkey in English, when referring to the country, and words related to people, language, culture, and ethnicity are rooted in Turk and Turkey. The adjective, as marked with the exclamation mark above, is still Turkish. Not… well, Türkiye didn’t offer any adjective. Neither did they offer any other words that would be derived from Türkiye.
It can’t be blindly assumed that a new name can’t be adopted. Changes in country names are nothing unusual, do happen, and do work. New generations of speakers come and they use a new word. Your grandparents would also think the same of word
Turkey, as to them it was
Ottomans (
Ottoman Empire). Now nobody is surprised with
Sri Lanka (formerly
Ceylon), somewhat less common
Czechia (in the past referred to with the unwieldy
Czech Republic),
Myanmar (
Burma),
Burkina Faso (
Upper Volta), or
Zimbabwe (
Rhodesia).
The main issue with adoption of Türkiye in English, outside of official contexts, is that the only accepted spelling includes letter ‘ü’ which most people can’t type on their keyboards or phones. The second problem is the ‘iy’ which can’t be easily derived from word’s sound.