if my car is under my parents name and i am not registeed as a driver with the insurance, would the insuance still have to cover

Your question is difficult to understand but I will try to explain some general concepts. Insurance coverage is contractual in nature. This means who is covered, and who is excluded from coverage, are found in the policy language itself. Normally, anyone driving the vehicle with the permission iof a covered person is also covered by the liability portion of the policy. Also, usally, the policies cover family members who live in the same house whether they are named or not. Look for a section of the policy entitled "Who is covered." Further, the insurance company has to send you a letter that specifies why they elected to deny coverage. Sometimes this letter is hard to understand because the language is so convoluted but you have to read it all the way through to make any sense of it. I rececommend that you take this letter and your insurance policy to a lawyer for review. But, just because your name on the title does not automatically make you a covered person under the policy. Again, take this into a lawyer you trust and have it reviewed before the person you hit sues you!