As far as i can tell, the Greek inhabitants of the Eastern Roman Empire, for most of its 1000 year duration, identified themselves as Romans. But despite that 1000 year proud (should be) Roman/Byzantine history, the people there at some point started identifying themselves as Greeks and wanting an Independent Greece. When and why did that transition from Roman to Greek happen?

When the 1821 Independence war happened, and the new nation emerged, it wasn't referred to as Roman or Byzantine (the name the Eastern Roman Empire was being identified by that point from most people if i am not mistaken), but instead Greek.

And what confuses me even more is that the "Megali Idea" concept that dominated greek politics for the next century, was all about restoring the old Byzantine territory and re-establishing Constantinople as a capital (thus resurrect the old empire if i understand correctly).

And please excuse in advance any potential ignorance of mine.