After the Ottomans conquered the Byzantine Empire, how did the people of the conquered territory identify themselves culturally/nationally? Did people there have a strong Roman/Byzantine identity before? If it went away, how long did the transition period take?
Not sure of the full answer here, but an important scholar of Islam, Jalal al-Din al-Rumi was known as "al-Rumi" because he came from Rum (the land of the Romans) as the Seljuks and Ottomans referred to Anatolia, even after its conquest.