The department shall file each application received and when satisfied as to the genuineness and regularity thereof, and that the applicant is entitled to register such vehicle and to the issuance of a certificate of title shall register the vehicle therein described and keep a record thereof in suitable books, on index cards, or by means of magnetic recording devices as follows:
(1) Under a distinctive registration number assigned to the vehicle;
(2) Alphabetically, under the name of the owner;
(3) Under the manufacturer's serial or identification number if available, otherwise any other identifying number of the vehicle; and
(4) In the discretion of the department, in any other manner it may deem desirable.