I study Turkish studies and have had the opportunity to see a few documentaries (in Turkish) about the former Ottoman ruling dynasty. I don't have them immediately accessible to me, but I can look around for them and also see if I can find some information for you in English.

One interesting thing to note about the former Ottoman dynasty is that they do not actually go by the surname Osmanlı, but rather by the surname Osmanoğlu, which means "son of Osman." After the collapse of the Empire, members of the family were exiled from what became the Turkish Republic in 1924. They generally scattered across Western Europe, the United States, and select parts of the Middle East. Specific areas I remember members of the family settling would be France (primarily southern France and the French Riviera), New York City, and Beirut.

I apologzie for the relatively brief response--hopefully, I'll be able to find my sources for you soon!

you have to bear in mind that surname was a relative new thing for turkey (there was no surnames in ottoman empire but titles and nicknames). the surname law came into effect in turkey as late as 1935. many people in the lost territories (e.g. balkans, arab lands etc.) of ottoman empire still use derived surnames from old nicknames and titles. in turkey however most people chose generic surnames rather than incorporating their old nicks/titles into surnames.