It would appear you have taken the correct steps to pick up the used car you purchased on Ebay. Though due to the fact that each state has their own licensing, registration and traffic laws we are unable to tell you for certain if you could legally drive home your new "used" car.
If the car has insurance on it and is still registered with a current inspection sticker and valid license plates then likely you would be able to drive it home and then proceed to register and tag it in your name however we would suggest contacting your state's Department of Motor Vehicles to make certain. There may be other steps you need to take in order to take possession of the car and legally drive it home that we are unaware of due to the varying state laws across the United States.
If you are driving the car with the previous owner’s plates on it then you will need to find out if these plates can be transferred into your name or if you will have to return them back to the seller for them to transfer or turn in themselves to the DMV. If they are not allowing you to use their license tags to drive home then you will need to check with the DMV about temporary tags or what you should do in order to legally transport the car back to your residence.
If your Ebay purchase is out of state then you may need to contact each state's DMV to make certain you are following the laws of both states when you pick up the vehicle and drive it home.
Hope you enjoy your Ebay purchase. Next time you want to comparison shop for auto insurance rates contact us for a quick quote.