Yesterday the man's lawyer, Peter Magee, argued against his client's name being publicised and for the woman's identity to be revealed.
The police wanted the man's interim name suppression to end, but the woman's to continue.
Judge Simon Maude ruled that there were insufficient grounds to continue with name suppression for the man or the woman and he ended the interim suppression orders.
However, Mr Magee and the police both indicated they may appeal the decision to the High Court.
Judge Maude continued interim name suppression, including name, address, occupation and any other details that may identify the man or woman, until 5pm on May 22.
If an appeal has not been lodged with the High Court by that time the suppression orders will lapse.
The specific charges the man faces will be back before the court on July 12.
It is possible the man will enter a plea to the charges at that hearing.
The man has been remanded on bail.
He was earlier ordered to surrender his passport and not to apply for another passport or travel document.
He was also ordered not to contact a list of people and associates named by the prosecution.