Hit , and select multiplayer. Join or create your own game. Hit again once you're in a game and select "Edit License Plate".
You'll have to complete milestones tied to license plate rewards to unlock backgrounds. Speed Points in single+multiplayer are linked, so if you've played the game at all, you should have at least "Running In" unlocked for reaching Speed Level 2. Select a plate and hit to apply.
Next, hit to edit plate registration. Enter anything you want and hit when you're satisfied. The achievement will then unlock.