Never seen this in Germany. Not that I remember, but most places, no, this doesn't happen.
"downstairs/apartment building's set of doorbells also proclaims last names, and are often ordered by floor"
They thought of that. So they mix it up, or just list, it has nothing to do with floors
"In fact, it's advised that you don't put any first initials/first names on your doorbell"
Correct, they usually put last names only.
Obviously, there's no standard nor convention, but Hausmeisters seem to find it convenient, and I like it when I can do that when visiting a friend for the first time.
Of course there are, however, apartments whose Haustür (the door to the apartment building) leads to several different buildings or staircases. In that case, good luck ever finding that person even if they want you to come visit.
What are you talking about? Every apartment building has a set of labeled doorbells at the ground floor.
So, in total, your name is three places in the apartment: at the entrance next to a doorbell (which effectively "calls" your flat), on your mailbox, and above the actual doorbell near your flat's front door.