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.
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.