Tennessee "corporation", "incorporated", "company", or the abbreviation "corp.", "inc.", "co.", or words or abbreviations of like import in another language (provided they are written in Roman characters or letters); existing corporations which were formed using only "limited" or "ltd" are not required to change their name § 48-14-101 Tennessee Code
Washington "corporation", "incorporated", "company", or "limited", or the abbreviation "corp.", "inc.", "co.", or "ltd."; must not include "Bank", "banking", "banker", "trust", "cooperative", or any combination of the words "industrial" and "loan", or any combination of any two or more of the words "building", "savings", "loan", "home", "association", and "society" § 23B.04.010 Revised Code of Washington
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.