LLC, LC, Ltd. Co., Limited Liability Company: a form of business whose owners enjoy limited liability, but which is not a corporation. Allowable abbreviations vary by state. Note that in some states Ltd. by itself is not a valid abbreviation for an LLC, because in some states (e.g. Texas), it may denote a corporation instead. See also Series LLC. For U.S. federal tax purposes, in general, an LLC with two or more members is treated as a partnership, and an LLC with one member is treated as a sole proprietorship.
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.
In this case, you need to write a remark about that circumstance on the Business Property Statement, or on an attachment to it. Also fill out Part III (Equipment Belonging To Others) of the form. If you own any small equipment, such as a printer, copier, etc., that you are using in the business, you should report these costs under Part II of the Business Property Statement and also Schedule A.