Police are keeping an eye out for breaches of a name suppression order in the Grace Millane case.
But they are yet to prosecute anyone, despite flagrant breaches.
Ms Millane's disappearance and the subsequent charging of a man with her murder have dominated headlines in the past week.
The alleged killer's plea for name suppression was initially rejected, but his lawyer appealed, forcing the judge to grant an interim 20-day suppression order so the High Court can take a look at the judge's decision.
That didn't stop international media from naming him, and Google even sent an email to subscribers of its 'trending' search topics with his name in the subject line.
Police told Newshub on Friday they are "continuing to monitor the situation regarding breaches of suppression orders in New Zealand".
"At this stage, we are not aware of anyone being charged in relation to a breach of suppression order.
"Police have the ability to charge a person for breaching a suppression order, provided there is sufficient evidence to do so."
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A spokesperson for the Solicitor-General told NZME it was up to police to prosecute breaches, of which there have reportedly been hundreds - not just on social media, but international news outlets.
Some UK sites which named the alleged killer have blocked their stories from being access in New Zealand, but can still be read on Google's caching service or by anyone disguising their location.
Google said there have been more than 100,000 searches for his name on its search engine, and it had not received a court order to block New Zealand users from finding articles about him. A number of Twitter users with their location as New Zealand have also named him.
Justice Minister Andrew Little earlier this week urged people - here and overseas - not to name him.
"It will not do justice to the Millane family if the accused in this case gets to walk away from facing justice because somebody else disclosed his details and he is able to say he won't get a fair trial," he told Newshub on Tuesday.
"That's why we have suppression rules. Like them or not, we have to abide by the ruling of the court."
The punishments for name suppression include up to six months in jail and $100,000 in fines.
Newshub.
