Unltd or Ultd (Unlimited/無限公司): similar to a limited liability company (Ltd) but whose members or shareholders do not benefit from limited liability should the company ever go into formal liquidation. It is not a requirement under company law to add or state the word or designation Unlimited (無限公司) or its abbreviations (Unltd or Ultd) at the ending of its legal company name, and most unlimited companies do not.
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
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.