In a sole proprietorship, the business owner and the business are one thing and there is no legal distinction between you (the owner) and the business.
This means you are legally liable for the business debts and legal proceedings of the business: your assets (car, house, and other personal property) also belong to the business.
In some cases, you may have to file a Fictitious Business Name (otherwise known as DBA: Doing Business As) with your local government agency. See permits section for more information.
In California, you may register your business as a sole proprietorship with your city/county. You can use your ITIN or SSN to register your business.