Do you need to be added to your parent's insurance in order to drive their car?

Yes.

Reason why you name should be listed in insurance policies of your parents

it's pretty standard rules for every insurance policies to say if a vehicle is provided for your regular use and you are not listed on the policy then the insurance company can deny coverage of your vehicle

insurance companies have their own rules. They put every rules what they want by insurance for any vehicle

Younger drivers are considered Higher risk, especially new drivers. If you want to drive your name should be listed with your parent's name in the insurance policies you can driver the car with out having to pay the bigger insurance premium. The law does not care if you do that. However, the insurance company does and you risk not being covered in the event of an accident. This means both you and your parents turn out to be personally responsible for just about all damage/injuries a person result in.

Your very best self is usually to expect to have a career and also pay out your folks to the elevated insurance plan high quality. They may list you on a policy.