If I am a taxi driver for Yellow cab , but I own the car I use, what do I put for business owner? Yellow cab or myself?

You would enter yourself as the business owner. You are a contract employee for Yellow cab so that would make you the "business owner".

As an independent contractor, without a specific name for your independent business, your own name is the business name and the business address is your home address unless you have an office of your own at a different location.