Yes, So long as you are also listed by name as a covered driver on your parents Policy and your parents have an insurable interest in your vehicle.
If you are a minor or a dependent still living at home then you might be able to get insurance cheaper through your parents than you could seperately.
You "by name" would need to be added along with your vehicle to your parents policy to be an insured driver.
If your trying to get insurance while
hiding the fact that your a driver, that is a well known form of Insurance Fraud by concealment. It's a Felony and you would not be covered.
I know if your under a certain age you can. I have a car UNDER MY NAME, and it's under my parents insurance. I think it might be 21 or 23 where that stops. It is NOT 18.