Prime Minister Jacinda Ardern has given an assurance to the New Zealand public that they will never hear her use the name of the man allegedly responsible for the Christchurch terror attack.

This comes amid mounting concern that the gunman plans to use his trial as a way to promote his extremist views.

Yesterday, the Herald revealed that accused gunman Brenton Tarrant planned to represent himself in court.

The duty lawyer, who represented Tarrant in court on Saturday, confirmed he was no longer acting for the man.

Richard Peters said that his job representing Tarrant ceased on Saturday – and that the accused gunman had told him he wanted to represent himself in future.

This raised the prospect of Tarrant conducting his own defence at trial and using the high-profile prosecution to promote his beliefs, which were detailed in a manifesto before Friday's shootings.

Speaking to media this morning, Ardern said this was "something that we need to acknowledge and do what we can to prevent the notoriety that this individual seeks".

She said the gunman "obviously had a range of reasons" for committing his act of terrorism.

"Lifting his profile was one of them," Ardern said. "That's something that we can absolutely deny him."

But when it comes to the alleged gunman's court appearances, Ardern said the media had a part to play in preventing the wider public from hearing his extremist views.

Asked what could be done to prevent the accused from having a platform, Ardern said this was something that was "very early on" in her thinking.

"I've only had beginnings of conversations – that's something I think we really will be looking to the media around its kind of coverage.

"Of course, people will want to know what is happening with the trial. But I would hope there are ways that it could be covered without adding to the notoriety that this individual seeks."

She said any decisions about having the trial behind closed doors was not up to her.

"That's why, as I say, this is a conversation I think really the media can play a strong role in."

"But the one thing I can assure you – you won't hear me speak his name."

Ardern has not mentioned the gunman's name in any of her media interviews or press stand-ups.