The court heard the man's family would suffer "devastating consequences"
Judges in the UK have reserved a decision on whether to allow a celebrity involved in alleged extra-marital activities to be identified.
It comes after the Supreme Court in London was told the man's family would suffer "devastating consequences" if an injunction preventing him from being named was lifted.
A lawyer representing the man, who has "young" children, said this would still be the case even though he has already been identified abroad and online.
Desmond Browne QC said there would be a "storm of harassment" if the injunction was discharged.
Supreme Court justices have been hearing a challenge by the celebrity - referred to as PJS - against a decision by the Court of Appeal that an order barring The Sun on Sunday from naming him should no longer apply.
Earlier this year, the newspaper sought to publish an account of the man's alleged sexual activities, but he argued he had a right to privacy and took legal action.
The newspaper won the first round in January when a High Court judge refused to impose an injunction. Two Court of Appeal judges later issued a ban protecting the man.
But on Monday, three appeal judges ruled it should be lifted following representations from the tabloid's publisher News Group Newspapers (NGN).
It argued the ban should end because the celebrity had been named in articles abroad - outside the legal jurisdiction of England and Wales - and his name could be found on the internet.
NGN maintains it would be in the public interest for it to publish the story and measures could be taken to protect the children.
Ultimately, it says, the case is about balancing rights.
Judges have revealed the man is in the entertainment business and that his spouse - referred to as YMA - is also well-known in the industry, and the couple have "young" children.
The injunction will remain in place pending the Supreme Court announces its decision.