Here
https://www.immigration.govt.nz/new-...emporary-visas is the INZ page that tells you about the circumstances in which you would need to apply for a variation of conditions. From what you have said, if the name of the employer is going to change, or the description of your duties, then probably you will need a VOC, but if it is both, you may need a new visa.
The thing to do is to talk to INZ. They are normally very helpful about arranging a necessary change-over, and they will tell you exactly how to proceed.