Police are expecting more women to come forward and report alleged violence at the hands of Grace Millane's killer now that his name has been made public.

And they have said they want to hear from any woman who has a story to tell about Jesse Shane Kempson - vowing to investigate every new allegation and provide other survivors the help and support they need.

The Herald can also reveal Millane's mother Gillian has been supporting other women who have come forward, encouraging them to report what happened to them and get the help they need.

Kempson could finally be identified today after his name suppression - put in place after his arrest for Millane's murder in December 2018 - lapsed.

After his first court appearance, a number of women came forward to complain to police.

He was charged in relation to two sexual assaults on other women including rape and violation and convicted after separate trials in the High Court at Auckland.

Kempson is appealing the conviction and sentence of the second and third cases but the details can be revealed today after the Supreme Court ordered name suppression for the killer to lapse.

Detective Inspector Scott Beard said now Kempson's name was public it was highly likely more women would come forward to report their experiences with him.

"After he was arrested more than a dozen women came forward, and there were others we identified through our investigations," he explained.

"By all means, if there's people out there who have been subjected to abuse and violence by Grace's murderer - tell us.

"Come forward and tell us, we will get you the support you need. Prosecuting him - that's not the main reason for coming forward, as we know the psychological affect on victims is significant.

"So come and see us and talk to us, tell us your story. We've heard it before, it's not going to be something new to us and we can get you the support that you need to move forward."

Beard said some women had felt guilt about not coming forward sooner.

However, Beard said: "From his actions and behaviour to his subsequent actions and reaction after he killed her - I have no doubt that If it wasn't Grace, it was going to be someone else.

"It was just a matter of time.

"And through the trials we - and the media - got a true insight to that."

Beard said Millane's mother has been in contact with the two other victims and supported them through their court processes.

• Grace Millane's murderer named, sexual violence trials revealed

"She told them they were strong enough to go to court, that 'you take control," he said.

Gillian Millane - whose husband David died last month after a battle with cancer - encouraged the women to stand up in court and hold their abuser to account.

And she encouraged others to come forward.

"If there are other women out there who are not sure if they should or want to come to police, we urge them to do so, they should not feel any responsibility or guilt regarding Grace Millane," said Beard.

"There is only one person responsible for Grace's death and he is behind bars, where he will remain for a long time."

Beard ran all three inquiries into Kempson's violent sexual offending and said if more women came forward, detectives would start the investigation process from the beginning.

Just because he had already been jailed did not mean he could not be held to account for any other crimes, the top cop said.

Beard told the Herald it was a relief that the secrecy around the rapist and murderer's name had ended.

"The murderer, that's what I call him - Grace's murderer, I don't put a name to him," he said.

"We totally understand and get the reasoning of the courts around suppression - and we understand how and why members of the public were frustrated.

"But we had total trust in the legal reasons for him to keep it until today."

Beard said a case where one offender stands trial on different matters was not unusual, nor was the suppression around identity.

The ongoing battle around name suppression - including multiple appeals and delays due to the Covid-19 pandemic - had been frustrating but his team were more focused on getting the convictions.

"It's been a long two years," he said.

"We were just happy we could show how good our cases were, they convicted on all of them without them being heard together."

After Beard received the Court of Appeal decision last week, he contacted Gillian Millane and the two survivors.

Police had kept them informed every step of the way through their respective cases.

"They knew exactly what was going on," he said.

The journey for Beard and his team had been "emotional" at times, particularly when Millane's father David died from cancer.

The lifting of suppression marked the end of this chapter for the investigation team, but they would never forget the case.

"This will allow people to move forward," said Beard.

"It sounds callous but it's our job - I deal with a lot of death and there will be more cases that will come up. I will stay in contact with the Millane family and keep supporting them - Gillian, Michael and his wife Victoria, Declan and his partner Jess and their wider family."