After you submit, wait for the new registration in the mail. It takes 2–6 weeks. If it doesn’t come, call. Don’t assume it’s lost in a black hole.
While you wait, keep a digital copy. A photo on your phone. That counts if a cop pulls you over. Usually.
And here’s the kicker: Update your voter registration too. Your car knows where you vote. Don’t make your car smarter than you.