Dol Guldur

[Kuruharan]

Maybe he's forgotten everything (except that name) before he came to Middle Earth.

I'm not sure "forgotten" is the word I'd use to describe it. "Dimmed" or "veiled" I think describes it more accurately.

It seems to me that it's the other way around

There is some merit in what you are saying, but Sauron and the Balrog had undergone *profound* changes since the time that they had sung the Music.

I think it would be similar to the way that Manwe failed to recognize Melkor when the Valar defeated him in the War of the Powers.