The department shall file each application received, and when satisfied as to the genuineness and regularity thereof, and that the applicant is entitled thereto, shall register the described vehicle and the owner in books or electronic data processing files or on index cards or film as follows:
1. Under a distinctive registration number assigned to the vehicle and its owner, referred to in this chapter as the registration number.
2. Alphabetically under the name of the owner.
3. Numerically by the serial or identification number of the vehicle.
4. In the discretion of the department, in any other manner it may deem desirable.