If you are not listed as a driver, you are not insured on that policy. Which means you're probably in violation of your lease agreement and you wouldn't receive coverage in the event of an accident. If you live with your boyfriend, you and your vehicle can be insured on the same policy. He would still get the same multi-vehicle discount. But if you don't live with him, there's no reason for him to insure the vehicle. You definitely need to get a policy that meets your lease agreement
and is in your name. You can compare rates here.