The division of motor vehicles shall file each application received and when satisfied as to its genuineness and regularity, and that the applicant is entitled to register the vehicle, shall register the vehicle and keep a record of it in suitable books or on index cards as follows:

(1)  Under a distinctive regulation number assigned to the vehicle;

(2)  Alphabetically, under the name of the owner;

(3)  Under the motor number if available, otherwise any other identifying number of the vehicle; and

(4)  In the discretion of the division of motor vehicles, in any other manner it may deem desirable.