Actually it's well established that psychopaths are well aware of their psychopathy and the easiest way to diagnose is to ask someone whether they think they are psychopathic (of course then you follow up to test that thesis..).

Yeah you're right but I would say the type of psychopath you're describing is very very rare. It's also a spectrum.

Most evil of the psychopathic nature are conducted by people nearer to the psychopathic end of the spectrum but they aren't quite totally psychopathic. They bridge that gap by justifying their actions with lies they tell themselves.

Hitler, for example was unlikely to be a psychopath, but the actions he committed makes it seem like he was one. He was also likely on the far end of the spectrum in terms of psychopathy and clearly he still had some story he used to justify his horrific actions.