Most car finance and auto loan companies as well as the insurance companies will want to have the owner of the car listed on the auto insurance.
So when someone finances the car they will usually need to have their name on the insurance policy until the financed car is paid for.
But the person can have the other person listed on the auto insurance of the financed car but the person financing the car must have their name on the auto insurance policy as well.
The person needs to have an insurable interest in the car which would be the person who financed it.
So if you have someone finance a car for you then they'll need there name on the insurance and you can add your name to the insurance as well.
However there is one insurance company I know of which is ESurance that will allow you to take out an insurance policy on a car you don't own.