Of course, the Ottomans weren’t the only ones playing this game; the Holy Roman Empire and to some extent Russia were also examples.
> For example, we don’t call it “Constantinople” any more
Not to detract from the rest of your point, but "Istanbul" actually comes from a Greek nickname meaning "to the city", and didn't even become the official name until 1930."THE ETYMOLOGY OF İSTANBUL: MAKING OPTIMAL USE OF THE EVIDENCE"
https://ruj.uj.edu.pl/xmlui/bitstream/handle/item/15924/stac...
(It disputes the details of the traditional 'to the city' etymology, but in the end proposes deriving from something else with very similar meaning, "στην Πόλι" (something maybe like 'sten Poli' but there are details of historical pronunciation in the article I didn't read closely) rather than "εἰς τὴν Πόλιν" [is timˈbolin].)
They did, but after half to a full millenium after the fall of the Roman Empire - so for those there it was a much more "recent" (for ancient peoples sense of historical time) affair.
>For example, we don’t call it “Constantinople” any more and the inhabitants of the region don’t seem to consider themselves descendants of Romans as much as Ottomans
Funnily enough, the Mehmed II (the conquestor of Constantinople) did call himself (among other things) "king of the romans" after that.
And the name Instabul itself comes from Constantinople (also known as "Pole" (The City, it being the big Apple of the area, where Instabul meant "in-sten-Pole" (to-the-City).
But yes, the current inhabitants of modern Turkey region don’t consider themselves descendants of Romans. But you can find some connection to other parts of the mediterranean and the levant.