Do you have to surrender a car when they show up for repossession?

The exact answer will vary by state. Each state has its own rules. You should be aware that when the repossession is ordered, the car is not yours any longer. They are asking for their car to be handed over.

The repo man cannot (in most states) cut fences, break locks, open garages, threaten or harass you. They can defend themselves if you become hostile or aggressive. They also can sit patiently and wait for you to take the car out and take it away.

In some states you can be required to pay the repo expenses, so think about that before making the guy come back several times.