Hide user name from login screen (no typing the name)?

I know that you can disable the "pre-typing" of the user name on the lock screen, so that it looks like this:

In that case you have to type both the user name and the password for unlocking.

But what I want is to not have to type the user name, but just hide it, so that it looks like this:

In this case, you'd just type the password to get in, but the user name would not be visible.

It would also be OK if the actual user name was replaced with something else, like "User" or a random set of characters.


Let me know on the off chance that something like this is possible.

Unfortunately, none of those do what I want. They're mostly just different ways to do what I wrote about, where the username has to be typed.