"(a normal user should not even know there exists such a thing as a short user name; all he should know about is his long/real user name)"

I disagree. I have never once typed my long name into my own computer for login or authorization, since I established it 7 years ago. And why would anyone want to do that when the short name is easier? But I do like to see my full name displayed where appropriate.

By "normal user", I meant a basic user who will log in by choosing his account from a list instead of having ot type his account name, or will even have autologin activated, and will never do remote login through a shell.
This kind of user won't use a separate admin account, so the name field of authorization dialogs will be pre-filled automatically for him with the right name (his).

For this type of user, having to type his user name happens very, very rarely (for the occasional AFP access to his computer, for example), so why confuse him with a short user name that he can't even change easily (but he is never told that during setup!) but will look ugly on his home folder?

Of course, power users will know about the short user name and use it, but it doesn't mean this implementation detail should be shown to all the other users.