Open the Advanced User Accounts panel by typing in netplwiz into the start menu search box, and hitting enter. Then click the Advanced tab, and you’ll see this:
Just check the box, and the next time you login, you’ll see the old familiar prompt.
Update
For a method that works all the time, type in secpol.msc into the start menu search box and then navigate to Local Policies \ Security Options.
Find the setting for “Interactive Logon: Do not display last user name” and change it to enabled.