Most of the changes happened gradually and most common form was getting Turkified rather than completely changing the name. For example Constantinople’s name was indeed not changed after it was conquered with time Ottomans Sultans referred to it as Konstantinye instead of Constantinople and Istanbul is believed to be some kind of a Greek slang word which was adopted by the Turkish Republic centuries after the conquest.

You also mention some Arab and Jewish cities not changing names while Greek ones do. One example you gave was Damascus which is utterly untrue because Damascus in Turkish is Şam and it’s been for a while, Jerusalem in Turkish is Kudüs and it’s been for a while. Alexandria is an exception with the name remaining but getting Turkified to Iskenderiye.

The reason for the name changing is simple Turkish common folk don’t speak the language of the conquered land and the name transform to what they call it over time and eventually becomes the accepted way of calling the city. This works like that in every other country at the time. No matter how much the ruling families or elites will insist on keeping the old name eventually the one common folks use will be adopted with time and It’s not intentional like you put it so Turks really as a whole didn’t change names and it was more a process not a decision taken by the Sultan.