The land of Rum
The name "Turkey" as referring to Muslim Anatolia appeared much earlier in Christian, especially "Frankish" (Western Europeans of the Catholic faith) historical literatures than in Muslim ones. The Muslim Turks preferred to refer the land of Anatolia as Rum, implying a separation between the concepts of the "Christian State of Rome" (Byzantium) and the "Land of Rome" (Anatolia). As Byzantine Iconia (Konya) fell to the Seljuq viceroyalty of Anatolia and became the Muslim "Sultanate of Rum" under a Seljuq prince, more and more Anatolian Turks identified themselves as "Rumi", not the least the world famous, Khorasan-born Sufi poet Mevlana Celaleddin now known by this nom de plume, who lived in Konya for half of his life.
Anatolia as the land of "Rum", but not as an ethnically homogeneous country of Turks is a subject of academic curiosity. The Khorasan-born Celaleddin, no doubt of Persian-Turkish heritage, learned not only to speak the local Turkish dialect of Konya, but also the Cappadocian Greek language widely spoken (the majority of the subjects of the Sultanate of Rum could be speaking diverse languages other than Turkish) in Southwestern Anatolia back then.
In early Ming China, the land of Anatolia was still assumed to be a region contested by several states: Ottoman, Timurid, Akkoyunlu etc, rather than a unified Ottoman Caliphate.

Turkia
It was only in the late Qing Era, that the name "Turkia" was reintroduced to China through Western writings. It is interesting to note that the first Chinese transliteration for "Turkia" was not the modern "Tu-er-qi", but the Tang era "Tu-jue", which denoted the Mongolian Steppes tribe of Turks, long predating the Turkish colonization of Anatolia. The Chinese reformist Kang Youwei wrote extensively on Ottoman issues, and named two of his major treatises "Journey to Tu-jue" and "The Imperial Review on History of the Weakening of Tu-jue" .
No doubt, West Europeans were the first to refer to the Land of Anatolia under the Ottomans as "Turkia". To them, the entire Ottoman sphere of influence was held under the sway of a barbarian horde of Turkic race and Islamic faith. In this sense, even loyal Wallachian and Phanariot princes and grandees, Muslim corsairs of Greek or Maghrebian origins, Janissary troops of Croat or Albanian birth and Western European converts into the Ottoman fold were "Turks".
However, to the Muslims themselves, the idea of lands of Anatolia, Iraq or Rumelia as "Turkia" was not even established before the Young Turks seized power from Sultan Abdulmecit in the late 1800s.
The Ottoman Turkish language, now academically referred to as "Osmanlica", was then indeed referred to as nothing but "Turki" or "Turkce", just like its close relative spoken by the Timurids, Chagatayids and Uzbeks. However, the vast Osmanlica or colloquial Turkish speaking subjects of the Ottoman Empire had a much weaker sense of common "Turkic" identity. First of all, Turkmen colonists who first entered Anatolia in the 1100s, having assimilated to the local cultures, social structures and gene pools of substratal indigenous populations, adopted entrenched "regional" or "localized" identities in a fashion analogous to the "Creolization" of European colonists in post-Columbian Americas. Secondly, the Ottomans being a beylik that first grew into prominence n the Rumelian (Balkan) Peninsula, naturally saw Anatolia, Caucasus and Iraq as no more "central" in the Ottoman Dar al-Islam than Rumelia. And Rumelia compared to Anatolia, has hardly ever been a land of majority Turkic population.
However, the "Creolized" sedentary people under Ottoman rule of probable Turkmen descent and Ottoman subjects of diverse origins who adopted Turkish as their primary language were not to easily accept "Turk" as their ethnic identity. During the Ottoman era, the ethnonym "Turk" designated nomadic Turkmens much in the same way "Arab" designated "Bedouines" as opposed to Levantines and Egyptians. These Turkmens are to be called "Yoruks" and Iraqi Turkmens in modern times, who have preserved distinctive Turkmen clans and social organizations. Most Turkish-speaking Ottoman subjects, by absorbing or being absorbed by indigenous substrates, had lost much of what defined the "Turkmen".
The ethnic identity "Turk" were not at all proper to these non-Muslims, until the secularization of the Turkish Republic by Ataturk and the calls of emancipation of non-Muslim communities to facilitate their assimilation into a modern secular "Turkish" nation.

The crumbling of an ethnically and religiously plural Ottoman Caliphate appeared to begin with the rigorous display of ethnic awareness by non-Muslim communities in Rumelia. Nations of the Orthodox Christian faith(s): Greeks, Serbians, Armenians, Bulgarians, became fully independent politically as well as culturally, under the encouragement by European Enlightenment ideals.
The national awakening of the Balkans made Anatolia, Caucasus, Iraq, Levant and Arabia extremely volatile. Throughout most part of the empire, loyalty to the Ottoman Sunni Muslim Caliphate was taken for granted of the Greek, Serbian, Assyrian, Armenian churches and the Sephardic Jews. Nor had the Sunni Levantine Arabs, Bedouines and Kurds any doubt that the Ottoman Caliph and the Askeriya elite he represented, were the leaders of their communities. The only element of dubious loyalty issue were the Shiites: Alevi "Kizilbash" (Red Cap Turkmens) who had strong leaning toward Shiite Persia. But the secession of the entire Balkan changed all that. Now the Caliph had to reconsider what defined loyalty to the Ottoman state. This was during the reign of Sultans Abdulhamit and Abdulmejit. Many mock "congresses" were convened with delegates representing loyal Ottoman Armenian, Arab, Kurdish and Turkish subjects, in order to discuss the a common "Ottoman" identity constructed on modern nationalist mode rather than along sectarian lines. But at the same time, these late Ottoman autocratic rulers also desired to play the role of Sunni Muslim Caliph to all the world's Sunni Muslims. Thus, an "Ottoman identity" during this time was obscured by the ambiguity as to what it meant to be loyal to the Ottoman Caliph, whether it was a religious affiliation or a modern secular nationalist one. Also, parochial, communal and partisan interests slowly pushed the multi-faith, multi-ethnic cooperation under "common Ottoman identity" into bitter bickering among linguistic and religious communities still part of the empire. This sow the seed not only for the later conflict between Muslim Turks and Christian Armenians, but also those among Sunni Muslim Turks, Kurds and Arabs. Indeed, divisions and mutual hostilities like these were unthinkable during earlier times of the empire, when every religious community, or "millet", had a proper place in the Islamic social system, and when Sunni Kurds, Turks and Arabs were part of the same "millet", rather than separate communities.