One important aspect is that NZ (and Australia as well IIRC), have always had laws that gave name suppression to people accused of a crime and its been illegal

One important aspect is that NZ (and Australia as well IIRC), have always had laws that gave name suppression to people accused of a crime and its been illegal to publish names of accused if they were granted name suppression. I think this is one of the primary cases how some of the censorship laws have been used.