Is it possible to have a car in your name and under parents insurance plan with you as driver out the being owned by parents?

Yes, this is possible. It's a common scenario. You own the car, but your parents add you to their insurance policy as a driver. The insurance covers the car, regardless of ownership, as long as you are listed as a driver on the policy. However, your parents will likely see a significant increase in their insurance premiums because they are insuring a vehicle that isn't owned by them and insuring a younger, less experienced driver.