The call was quickly taken up by social media users and may pressure authorities to allow her identity to be revealed.
The 23-year-old physiotherapy student died on December 28 in a Singapore hospital, two weeks after a gang rape on a bus in New Delhi that ignited protests across India and government promises of tougher punishments.
The woman's father said: "My daughter didn't do anything wrong, she died while protecting herself. I am proud of her.
"Revealing her name will give courage to other women who have survived these attacks. They will find strength from my daughter."
A British paper named the father and his daughter, saying the father had given permission.
After the interview the woman's name was the top trending topic among Indian Twitter users.
Mainstream Indian media did not identify her, however.
Indian law generally prohibits identification of sex-crime victims to protect their privacy in a country where the social stigma associated with rape can be devastating.
Five men have been charged with gang rape and murder and will appear in a New Delhi court today to hear the charges.
Prosecutors say they have matched DNA from her blood to blood found on the accused's clothes, and on hers, which one of the men had allegedly tried to burn to destroy as evidence.
"The bloodstain appearing on the burnt cloth has been tallied with the blood sample of the victim," prosecutor Rajiv Mohan told reporters on Saturday.