A lawyer for the women, Nikki Pender today said the victims were not consulted before that suppression order was made.
After a three-day jury trial at Christchurch District Court in 1995, the man was convicted on five counts of sexual offending and jailed for 12 months.
The suppression order was never reassessed and remained in place.
The man's criminal record was later "circulated widely", Ms Pender said.
The Sensible Sentencing Trust (SST) published it on its website.
In 2010, a complaint over SST's publication was lodged with the Privacy Commissioner.
Later, the Human Rights Commission also laid proceedings against SST for breach of human rights.
SST unsuccessfully appealed the orders and removed the man's details from their website.
Meanwhile, the sisters were "largely oblivious" to the actions.
In 2013, they applied to become party to the privacy proceedings.
They also applied to Christchurch District Court for an order permitting publication of their names, which was later granted.
Today, Ms Pender said that "at a very high level" the original suppression order was "inappropriate".
Furthermore, it should never have remained in place, she argued, and was again assessed as being inappropriate once the sisters themselves had their own name suppression lifted.
Ms Pender regarded today's legal action as "a test case", arguing when victims have name suppression lifted, it should mean that the offender should also have their name suppression automatically dropped.
"We say [name suppression] was never appropriate but certainly now it is no longer appropriate," Ms Pender said.
Since he was sentenced the man has been able to live a life on a "false premise", Ms Pender said, with people not knowing is a convicted sex offender.
The man's lawyer, Jonathan Eaton QC told the court that the sisters' bid to have their attacker's name suppression revoked is "grossly inappropriate and unfair", given the "extraordinary" 20-year delay in lodging the court action.
While the sisters claimed it was a test case, Mr Eaton said it might be more appropriately be described as a "protest case".
The lawyer argued that there would be a "real unfairness" to the man if the suppression order was to be revoked.
"The passage of time and its impact on memory, the emotional response of the applicants and the media hype all conspire to remove any prospect this case could be fairly reported in 2015," his submission stated.
"The scope... the potential, if the applicants are successful here, is extraordinary."
Justice Cameron Mander reserved his decision.
