You can purchase your own insurance if your register a car in your name. But typically the insurance company will want you to list all of the household residents, this is also true for your parent's policy to list you as a household member as well. Disclosing this information protects both you and the insurance carrier.

If you are still driving your parents cars as well as your own it is likely you all will have to listed on each other's policies. The best way to get an exact answer to your question is for you to contact your insurance agent. You might find out it is cheaper for you to remain on your parent's policy and pay them for your portion instead of getting your own.

You will need to contact your insurance company or agent to determine your specific insurance needs.