Media reports quoted the dead raped victim's family members, as saying on Wednesday that they have no objection to the move and added that it would be an honour to the girl.
Family members of the 23-year-old woman who died 13 days after being gang raped on the night of December 16, have reportedly welcomed Union Human Resource Development Minister Shashi Tharoor's suggestion of naming the revised anti-rape law after their daughter.
"If her name is made public for this purpose, they have no objection to it," the family members said.
"If the government names the revised anti-rape law after her, we have no objection and it would be an honour to her," said her father.
Tharoor had on Tuesday favoured making public the identity of the gang-rape victim wondering what interest was served by keeping her name under wraps.
Tharoor had also said the revised anti-rape legislation should be named after the victim if her parents do not have any objection.
"Wondering what interest is served by continuing anonymity of #DelhGangRape victim. Why not name and honour her as a real person w/own identity?" he asked on micro-blogging site Twitter.
"Unless her parents object, she should be honoured and the revised anti-rape law named after her. She was a human being w/a name, not just a symbol," Tharoor, who is known for speaking his mind, said.
Asked about the financial assistance of Rs.20 lakh announced by the Uttar Pradesh Government and assistance of Rs.15 lakh and job announced by Delhi Government, the dead woman's brother said though announcements have been made, they are yet to receive the assistance.
The girl's father said he was satisfied with the announcements made by the government.
The family members termed as misleading reports in the media that the girl was about to get married.
On a question regarding police charge sheet in the case, the brother said they do not want to comment on the issue and only want justice.
Responding to Tharoor's tweet on Tuesday, former IPS officer, and now social and civil rights activist, Kiran Bedi welcomed the suggestion.
Bedi said: "What Tharoor has said, may be unique in India, but it is not new in the world. Many of the American laws, like the Megan Law, the Jessica Law and the Brady Law have been so named to perpetuate the memory and suffering of the victims, and also to remember the spirit behind the law. I would support Tharoor's suggestion, as it is a good idea".
Bedi further said: "As far as this case is concern, we have already calling her Nirbhaya. If her parents don't allow the name to be known, we can call it the Nirbhya Law. But if they do allow, I think the law should be named in her memory out of deep respect."
Union Minister for Information and Broadcasting Manish Tewari said: "I don't want to go in the debate what someone has said or has not said. The real tribute to our sister, who lost her life, would be to update our laws, to make them more stringent and to ensure our judicial processes deliver verdicts as speedily as possible."
BJP spokesman Shahnawaz Hussain said naming the victim would be a wrong step and would contravene court orders. He said that as a government minister, Tharoor should not be making such an irresponsible demand in his public or private capacity.
He said the BJP does not agree with Tharoor, and added that there were court orders in this regard.