What is the ruling on buying a car by paying 20% upfront and the rest in installments, with the car remaining in the company's name until the full amount is paid, and without requiring a final payment upon transfer of ownership?

There is no objection to purchasing a car from dealerships where the seller retains the vehicle's registration (istimara) in their name. This transaction is Islamically permissible, and the seller's retention of the registration does not affect the sale. It falls under the category of mortgaging the sold item with the seller to guarantee their right, and this is permissible.