Depends. Around here it's the Hochbahn. Wuppertal has the Schwebebahn, and a long time ago the Köln-Bonner Eisenbahn had the Silberpfeil racing along the Rheinuferbahn.
I'm only aware of one "Hochbahn" and that's just the name of the company operating the U-Bahn.
Yes? The name being a result of the way it operated at first, and still does so, in parts?