The Advertising Standards Authority (ASA) regulates the advertising industry in New Zealand. They have a number of different codes of practice for different types of advertisements. For health claims, the most relevant codes are the Therapeutic Products Advertising Code and the Therapeutic Services Advertising Code.
You can lodge a complaint with the ASA via a form on their website: Make a complaint
The ASA can’t consider complaints about the name of a product or claims made on its packaging. Complaints about these should instead be directed to the Commerce Commission.