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.
Maine words or abbreviations of words that describe the nature of the entity, including "professional association", "corporation", "company", "incorporated", "chartered", "limited", "limited partnership", "limited liability company", "professional limited liability company", "limited liability partnership", "registered limited liability partnership", "service corporation" or "professional corporation"; beginning July 1, 2007, may also include "limited liability limited partnership" for business corporations: Title 13-C § 401 Maine Revised Statutes; for non-profit corporations: Title 13-B § 301-A Maine Revised Statutes
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.