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In February, the 28-year-old man was sentenced to life in prison with a minimum period of 17 years for murdering Millane in Auckland in 2018.
He was convicted in November 2019 after a high-profile trial, which gained international attention, for strangling her to death in an Auckland hotel room.
In August this year, the killer took his case to the Court of Appeal in an attempt to overturn his murder conviction and sentence.
Yesterday, the Court of Appeal's president Justice Stephen Kós, alongside Justice Patricia Courtney and Justice Mark Cooper, also ruled the murderer's interim name suppression would lapse at the same time.
But the killer did not bow to the order and asked the Supreme Court to continue his suppression until a second appeal can be heard.
Just before 11am, that court made an interim order suppressing his name until further order of the court.
Millane, who had been travelling the world, went missing on the eve of her 22nd birthday in December 2018.
She had matched with her killer on the dating app Tinder before they met near a Christmas tree under Auckland's Sky Tower and spent the night drinking at nearby bars.
Millane was last seen alive on CCTV with her murderer, walking towards his downtown Auckland apartment.
But the university graduate would never leave the room alive - her body later found dumped in a shallow grave in the Waitākere Ranges.
"Exactly what happened from the moment Miss Millane first stepped into [the apartment] we will never know," the trial judge, Justice Simon Moore, said at the killer's sentencing.
"Only two people were witness to those events and one is not alive to tell us.... We do not know if Miss Millane struggled but it is likely she did."
The killer has continued to claim he is innocent and controversially argued at trial that Millane died due to complications from consensual sex while both were highly intoxicated and engaged in BDSM.
In a statement provided to the New Zealand Herald Grace Millane's family they thanked the Court of Appeal judges and others involved with the case.
"We are pleased at the outcome that has been reached today and would like to take this opportunity once again to thank Justice Stephen Kos, Justice Patricia Courtney and Justice Mark Cooper; The Crown prosecution team Brian Dickey and Robin McCoubrey; Auckland City District Police, especially Detective inspector Scott Beard, Detective Senior Sergeant Greg Brand, Detective Sergeant Tony McKenzie and Detective Toni Jordan for their hard work, dedication and unflinching support," the family said.
"We would also like to thank the people of New Zealand for the love and support they have shown to Grace and our family over the last two years."
Millane's family said: "Grace was a kind, fun-loving daughter, sister, granddaughter, niece, aunty, cousin and friend with her whole life ahead of her.
"She was enjoying the first of what would have been a lifetime of adventures before her life was so cruelly and brutally cut short by her murderer."
The Millane family said the young woman had a sense of fun, adventure, and loved travel and exploring.
"Along with her ability to light up any room she walked into it with her generosity of spirit, are memories we as a family cherish and how we will forever remember her."
The Millane family said while the focus would "inevitably be on the outcome of today's legal process" they had their girl at the forefront of their minds.
"As a family our hearts and our love will always be with our beautiful Grace," they said.
"Grace, you are, and will always be, our sunshine."
As the matter of name suppression is still to be dealt with by the court, police were unable to comment on the case or outcome.