No, at no point during the lease agreement does one actually own the vehicle, it remains the property of the leasing company. What that means is that the dealership or fleet leasing company owns the vehicle and is legally responsible for it. A vehicle's title is registered in the name of the owner. With a leased vehicle, the leasing company holds the registration, so their name will appear on the title. Leased vehicles for trust or business purposes must be leased under the trust or business name from the original contract, it cannot often be transferred to a new entity without permission from the leasing company.