Edit: reading some other comments ... I'm talking about the traditional financed purchase of a car, not a lease. Agree that for a leased car (which is quite common now though I've never done it), the ownership stays with the leasing entity.
When you live in a title-holding state, the title will be issued to the registered owner/operator of the car, regardless of lien holder. Though your lien holder will receive a separate document verifying their connection to the loan, you will be in possession of the title itself.
There are only nine title-holding states: Kentucky, Maryland, Michigan, Minnesota, Missouri, Montana, New York, Oklahoma, Wisconsin. In the other 41 states, titles are issued to the lien holder of your vehicle until the loan is fully paid off.
From: https://www.rategenius.com/resources/titles/#:~:text=There%2....
The used market is likely different but for new cars from Dealerships, GM Financial, Toyota Financial, Ford Credit etc are Billion Dollar subsidiaries.