Hit right on the dpad, and select multiplayer. Join or create your own game.
Hit right on the dpad again 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 A to apply.
Next, hit X to edit plate registration. Enter anything you want and hit START when you're satisfied. The achievement will then unlock.