The Turks did not displace the people of Anatolia upon their arrival and throughout the Seljuk and Ottoman Empire.
Most of the "Turks" in Turkey today Turkified Anatolians to a major extent and Muhacirs from the Balkans,Crimea and the Caucasus to a minor extent.
So,Anatolia only its native population with exchange population of the Greeks to Greece and the massacres of the Armenians and Assyrians.
The Turkic people who conquered Anatolia,were small in numbers,but superior in warfare.
So Islamization was the Turkifying key.But it should be remembered that people did not recognize themselves by ethnicity in the Ottoman Empire,but religion,the millet system.So since Muslims were taking direct orders from the Sultan,the Turkish language was acquired.Though not all Anatolian Muslims spoke Turkish or Osmanli.
The word Turk was not used by the Ottomans but foreigners saw them as "Turks" including in the Balkans where converting to Islam means you have "turned Turk".Turk was a derogatary word used to the peasants in Anatolia who were uncivilized and wild(among the Ottomans).
It was with Mustafa Kemal Ataturk,did the identity "Turk" really came alive.As citizen of the Republic of Turkey.