Many of the protesters say that women are viewed as second-class citizens
An Indian minister has called on the authorities to reveal the name of the Delhi gang-rape victim so that a new anti-rape law can be named after her.
Junior Education Minister Shashi Tharoor said unless the parents of the the 23-year-old medical student objected, she should be honoured.
The victim died over the weekend in a Singapore hospital where she was being treated for severe injuries.
The 16 December attack in a bus has caused a national outcry.
The woman and a male friend had been to see a film when they boarded the bus in the Munirka area of Delhi, intending to travel to Dwarka in the south-west of the city.
Police said she was raped for nearly an hour, and both she and her companion were beaten with iron bars, then thrown out of the moving bus into the street.
On Tuesday, police sources said the driver of the bus had tried to run her over after throwing her out, but she was saved by her friend, Press Trust of India (PTI) reported.
Police are expected to formally charge five of six suspects with murder on Thursday. If convicted, they could face the death penalty, which is rarely carried out in India.
The sixth suspect is reported to be under 18 and a juvenile. Police have ordered a bone test for him to confirm his age.
'Name and honour her'
"Wondering what interest is served by continuing anonymity of the Delhi gang rape victim. Why not name and honour her as a real person with own identity?" Mr Tharoor wrote on the micro-blogging site Twitter late on Tuesday.
"Unless her parents object, she should be honoured and the revised anti-rape law named after her. She was a human being with a name, not just a symbol," he wrote.
Social activist and former police officer Kiran Bedi supported Mr Tharoor's idea.
"What Mr Tharoor has said is maybe unique to India, but is not unique in the world," Reuters quoted her as saying.
"Many of the American laws... which have been made to perpetuate the memory or the suffering of the victim, only to remember that this is what happened and this is the spirit behind the law... I think it's a good idea," she said.
But some critics called Mr Tharoor's suggestion "deplorable" and India's main opposition Bharatiya Janata Party vowed to "oppose any such move".
On Tuesday, the victim's ashes were scattered by her family in the river Ganges.
The brutal assault of the woman has sparked massive public outrage in the country.
It led to huge demonstrations with protesters expressing anger over attitudes to women in India and calling for changes to the laws on violence against women.
The Indian government was also heavily criticised for its response to the attack, which many called "slow" and inadequate.
According to official figures, a woman is raped in Delhi every 14 hours, while women across the country say they are frequently subjected to sexual intimidation and violence.
Officials have since announced a series of measures intended to make the city safer for women.
These include more police night patrols, checks on bus drivers and their assistants, and the banning of buses with tinted windows or curtains.
The government has also set up a committee under a retired Supreme Court judge to recommend changes to the anti-rape law.
Late on Monday, the authorities in Delhi launched a new telephone helpline for women in distress. The 24-hour helpline number 181 will operate out of Delhi Chief Minister Sheila Dikshit's office and will be connected with all the 185 police stations across the city.
But many of the protesters say that women are viewed as second-class citizens, and that a fundamental change in culture and attitudes, backed up by law, is needed to protect them.