Version 13 of Linux Mint (Maya) uses the MDM login manager that requires you to enter the username of the user you want to log in to in addition to your password which might annoy a few people. Although it is possible to display a user list, the way of achieving this is quite circumstantial and involves editing an XML file which isn't the user-friendliest way.
Instead, you can also install the same login screen Ubuntu uses, which is lightdm:
To install it, just open a terminal and enter following:
sudo apt-get install lightdm
After the installation, you will be asked which of the installed login managers you would like to use, the original one (mdm) or the new one you just installed (lightdm) - pick lightdm here by selecting it and hitting Enter:
The next time you have to log in, you'll see your new login screen!