In their first interaction with media at their home village in Ballia district, Uttar Pradesh, after the death of the 23-year-old, her father and brother said they had no objection if her name was revealed in the process for making such a law.
Her identity has not been revealed and she is being referred to by various pseudonyms like 'Nirbhaya' and 'Abhaya'.
They also hoped that the government would act swiftly in this direction and ensure that girls and women across the country were made safer.
"In case an anti-rape law was named after my daughter, it will be a befitting honour for the spirit of my brave daughter," her father told media persons.
Shiv Mandir Singh, the gram pradhan (village head), has already named the primary school in the village after the deceased rape victim.
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Tharoor had stoked controversy by suggesting that the revised anti-rape law be named after the victim, and added that this should be done if her parents had no objection.
Officials, however say, naming of any section in the Indian Penal Code (IPC) or CrPC (Criminal Procedure Code) after a particular person might be very difficult as there is no precedent of this kind.
The woman was gang-raped and tortured in a moving bus in New Delhi Dec 16, 2012, and passed away Dec 29 in a Singapore hospital where she was shifted for better treatment.
The rape and the subsequent death of the woman had triggered a national outcry, with people demanding immediate action against her attackers and a revised anti-rape law.