What is the best way to get your license plate number if you don't have the plate? Report the stolen plates to the police. They should be able to figure out what it was. If they weren't stolen, contact your department of motor vehicles right away to report the plates lost. They can look them up by your name (assuming you're the registered owner) and/or the VIN on the car.
See who accessed your driver's license. If you want to see who's accessed your driver's license information, all you have to do. Driver's License Printer Stolen and Recovered. Of all the times anyone has asked you to produce your driver's license. Terrorists Don't Do Movie Plots; more.
You may have to pay a fee for your carelessness in that case. In either case you don't want plates registered to you just floating around out there.