OS X has two different usernames. One is a "Friendly" full name, as shown in the Users and Groups system preference. The other is the Unix level username. Unix usernames on OS X won't have a space in the name, and tend to be all lower case. The users on disk home folder will use the unix name, instead of the full name. On top of that, there is a user ID (a number, also from the unix side), and a UUID (more used with directory services like Active Directory).
From your description, it sounds like the full name was changed, but not every service on the machine was made aware of the change. This might indeed be a bug you have discovered. The login screens (and switch user off the screensaver lock) will accept the friendly name and try and resolve it to the unix name. They also accept the unix name directly.
To see the unix name, right click the account in Users & Groups and choose advanced options. I highly recommend not touching anything in that screen, as it can break things.
BTW, how do I remove the login screen from after the screensaver mode?
I'm going to answer this more in a "teach a man to fish" manner. Open System Preferences, and type in something to search for in the spotlight dialog in the upper right.