There isn't an official medical term for this. It is mostly just called fear of driving or driving phobia. Some terms have been made up for related problems, such as tachiophobia or fear of speed, and amaxophobia for fear of riding in a vehicle.
This may be because fear of driving is a modern phenomenon, and phobia terms derive from ancient Greek. Of course people 'drove' in vehicles pulled by horses etc, but the fear of driving that affects many people today is usually about speed, pressure from other drivers and fear of coping with the car's technology. You can find Ancient Greek words related to driving here, but they don't really convey the sense of driving as we understand it.
Driving phobia is surprisingly common - many people are at least mildly phobic about driving, but often feel embarrassed to admit it, and others find it so terrifying that they don't drive at all. You can learn more about this problem here.