Despite being a relatively new option, the limited liability company (LLC) is now one of the most popular business structures among smaller organizations. While allowing business owners to remain free from a great deal of the regulations imposed on other types of companies, it still provides limited liability protection for its owners (members). This means that the personal assets of an LLC's ownership cannot be collected to fulfill the debts of the business.
Your name must be unique, and not deceptively similar, to any other trademarked name or business. It is also required that your name not be used to intentionally misrepresent the products or services you offer. For LLCs, nearly all states will also require you to add a signifier of your limited liability status, such as "LLC" or "L.L.C." to the end of your company's name. You may be able to operate under a name other than your formal LLC name by applying for and using a dba.
On the other hand, if you are not responsible for its tax, then you should declare the equipment in Part III of the Business Property Statement (Equipment belonging to others). Where equipment is declared in Part III of the Business Property Statement, the Assessor will also send a Notice to File to the person reported as the equipment's actual owner.