Once you pay off your car the bank gives you something to say that you are aloud to sell your car. What is that called? I am not talking about the title.
Up here we call it a Release of Interest. Which, does just that... its a letter from the financial institution advising that they no longer have a financial interest in your vehicle. You can then take that letter to the licensing office and have the ownership/registration/title of the vehicle changed solely into your name, and you can remove the financial institutions name from it.
At the least you just need to sign the title over, but most states also have an additional form (many times not even something you turn in to the DMV, but just something that the buyer and seller both sign as proof of transaction), and that goes by many names. check out your states DMV website and there should be a link to forms regarding selling of your vehicle