How to make the login window display list of users and name and password?
As you have discovered, the choices are:

A list of users with their icon

--OR--

A name and password box

What you see at school is the "other" user - user info is stored on a network server, the complete list is both unreachable and potentially far too long to simply scroll through.

It's certainly possible, just get the "Server" application from the App Store and set up your own machine as a server.