The family members of the 23-year-old girl said that "if her name is made public for this purpose, they have no objection to it".
Talking to media, the father and brother of the girl said that "if the government names the revised anti-rape law after her, they have no objection and it would be an honour to her".
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, the Minister of State for Human Resources Development, 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&honour her as a real person w/own identity?" he asked on micro-blogging site Twitter.
"Unless her parents object, she should be honoured&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.
On reports of Telugu filmmaker Ramana Gaddam planning to make changes in his upcoming film to highlight the brutal gangrape, the girl's brother said before doing so he should meet them and give information about the storyline.
He said the director would have to clarify what he wants to portray in the movie.
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 brother said though announcements have been made, they are yet to receive the assistance.
However, 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.