You can turn on displaying the Owner field on the Vehicle Info screen, and specify that it must not be empty when you save inspections and work orders as final.
On the Company tab, click Service Request Types, Inspection Types, or Work Order Types depending on which settings you want to edit.
Click the Settings link in the Vehicle Info column next to the appropriate service request type, inspection type, or work order type.
On the Vehicle Info Settings page, select the check box in the Visible column and in the Required column next to the Owner field, and then click Update.