If you were to get the company name on your contract changed, you could trigger the need for a VOC on your present work visa
https://www.immigration.govt.nz/new-...c-are-changing, so that's not desirable. The most important thing for your application is to make it as easy as possible for the INZ CO to tick the necessary boxes - for everything to be clearly understandable. Is it possible for your payslip to note that your work is for companies A, B and C? Also, you could cover this by an explanatory note, and having the owner or general manager, whoever is given as the contact, ready prepared to confirm what their arrangement is with you.