Louisiana (except for railroad, telegraph and telephone corporations) "Corporation", "Incorporated" or "Limited", or the abbreviation of any of those words, or may contain instead the word "Company" or the abbreviation "Co." if the latter word or abbreviation is not immediately preceded by the word "and" or the symbol "&". No corporate name shall contain the phrase "doing business as" or the abbreviation "d/b/a". Only a bank or bank holding company is allowed to use any of "bank", "banker", "banking", "savings", "safe deposit", "trust", "trustee", "building and loan", "homestead", "credit union", "insurance", "casualty", "redevelopment corporation", or "electric cooperative". § 12:23 Louisiana Revised Statutes
A partnership is a business relationship entered into by a formal agreement between two or more persons or corporations carrying on a business in common. The capital for a partnership is provided by the partners who are liable for the total debts of the firms and who share the profits and losses of the business concern according to the terms of the partnership agreement.
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.