After you create your Sim, type in a last name, such as "y" or something similar. Move the pointer over the "Okay". Press BACKSPACE, then quickly select "Okay". If done correctly, you should have a Sim with no last name.
After making your family, type in one letter for a last name. Press BACKSPACE then automatically click "OK". If timed correctly, you should be at the "Create a Family" screen with no last name.
To have a Sim without a last name, press SPACE once.