As a person who is Swiss and has lived a while in Japan, everyone says “Heidi”. I think Heidi/the alps is the biggest stereotype of Switzerland to japanese people, not banking.
Same here, but I've noticed that, at least from my circle here, people don't know too much about countries in Europe. Not that they really should, I guess. I'm from the Czech Republic, and usually I should point it on a map for people to understand better where it is.