Corp., Inc., Corporation, Incorporated: used to denote corporations (public or otherwise). These are the only terms universally accepted by all 51 corporation chartering jurisdictions in the United States. However, in some states other suffixes may be used to identify a corporation, such as Ltd., Co./Company, or the Italian term S.p.A. (in Connecticut; see under Italy). Some states that allow the use of "Company" prohibit the use of "and Company", "and Co.", "& Company" or "& Co.". In most states sole proprietorships and partnerships may register a fictitious "doing business as" name with the word "Company" in it. For a full list of allowed designations by state, see the table below.
It should also be noted that the state of New York requires limited liability companies to comply with an unusually strict set of publication requirements. In addition to publishing notices in two papers in the county in which your business is forming, you will also be required to provide proof of this to New York’s Department of State within 120 days of becoming officially recognized as a business. Failing to do so can result in suspension of your right to conduct business in the state.
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.