Western Tourkia was a term given to Hungarians by the Byzantines Eastern Tourkia was a term given to Khazars by the Byzantines Turcarum Imperium ‘Turkish Empire’ (and other variants), although not used by Ottomans, it was given by the Europeans. They were also referred to Turkey from late 19th centuries.
Turkey of course Al-Dawlat al-Turkiyya was a term given at that time to mamluks, meaning state of Turks or it can be said ‘Turkey’ as well in modern terminology, because of the ruling class being Turkic. The term Turkestan comes from Persian sources, Tujue from Chinese and Türük el (land of Turks) can be found in Bilge Khagan inscriptions