The appellant's lawyer, Christopher Wilkinson-Smith, said he had instructions to seek the recusal of Justice Helen Winkelmann, who, he said, had had "quite extensive involvement" as a High Court judge in his client's case.
The lawyer said he had been asked to raise the issue only 10 minutes before the hearing started.
Justices Ellen France and John Wild discussed the issue with Justice Winkelmann.
Justice Wild said the decision on recusal was one for his colleague herself.
He said she had mulled over the issue earlier.
"All three of us already thought about it. Justice Winkelmann declines to recuse herself," he said.
"We will include in our judgment reasons for that ... they are essentially that a judge's previous involvement in the case does not normally provide a basis or a ground for recusal."
Justice Wild said there was no evidence Justice Winkelmann would not be "objective" about the application for continued secrecy relating to the appellant's identity.
Mr Wilkinson-Smith said name suppression was necessary to protect the integrity of any future appeal against his client's sentence.
"Effectively he will apply for a retrial," he said.
The appellant could apply for that retrial only after he was sentenced. Sentencing was expected to happen in August.
Tania Goatley, of the law firm Bell Gully, appeared for media organisations opposed to name suppression.
She said the Criminal Procedure Act allowed the media to appeal against the suppression order.
"Suppression for offenders convicted of serious crimes is very rare," Ms Goatley added.
Kieran Raftery, for the Crown, said the "very murder of Mrs Gotingco was itself a newsworthy event". He also said any retrial was a "remote possibility" rather than a certainty.
Justice Wild ordered non-publication of some aspects and arguments of the name-suppression appeal. The judges said they hoped to release their decision soon.
Throughout the four-week trial, the media were allowed to publish images of the appellant's face but his name remained suppressed.
After the jury returned its verdicts in the High Court, Justice Timothy Brewer said there was no reason for the defendant's name suppression to continue.
