It doesn’t matter whose name you write when repaying the loan. As long as the corresponding money arrives in your account every month, the bank can directly transfer it yourself!
Whose name has an impact!
However, after the loan is exchanged, you must promptly go to the unit where you purchased the car to handle the "cancellation of vehicle mortgage" business.
Otherwise, what happens when the car is sold? The bank will be the first beneficiary, not you!