The issue relates to last week's legislative approval of rules requiring users to provide their actual names to identify themselves to providers of Internet and telecommunications services.
The Xinhua News Agency reported participants in the public "heated discussion" include both supporters and opponents of the new policy.
China has more than half a billion online users and already has stringent Internet censorship.
Xinhua reported some online users say the new policy will make them more cautious when airing their views, but others claimed the concern was unnecessary.
"Zhang Lifan," writing in the popular Internet portal Sina.com, was quoted as saying the new policy will affect online communication and reduce user participation in political discussions.
However, Yin Yungong, director of the Institute of Journalism and Communication at the official Chinese Academy of Social Sciences, said the policy will help reduce malicious rumors at the source, Xinhua said.
"The policy will ensure online information spreads in an orderly and safe way," Yin said, adding users will gradually get used to it.
Xinhua said several Chinese telecom service providers already require real-name registration.
The report said Sina Weibo, a popular micro blogging site used by whistle-blowers to expose official corruption, began requiring real-name registration since the start of this year.
Both sides in the discussion, however, insist on strict protection of their online ID information, with some expressing concern whether the government would be able to give that assurance.
"I doubt the government's ability to ensure the security of our information," wrote a Sina Weibo user.
Xinhua quoted a May survey by the China Center for Information Industry Development in which more than 60 percent of respondents complained of theft of their personal information.
The report also quoted a commentary on people.com.cn that the new policy is aimed at strengthening protection of online information. It said most people who shop online have used their real identities.
Among censorship activities under the current practice in the Communist country, Chinese censors block websites that discuss such topics as Tibetan spiritual leader the Dalai Lama or the 1989 crackdown on the Tiananmen Square democracy protesters, The New York Times reported. The report said through last year, such restrictions only became tighter.
China went through leadership transition in November during the Communist Party congress, which raised hopes the new team led by reformist Xi Jingping would ease the restrictions, but so far there have been no major changes.
The Voice of America said the new rules come in the wake of a crackdown on virtual private networks, or VPNs, which Web users need to get around China's so-called "Great Firewall."
Duncan Clark, a senior adviser to Stanford University's Graduate School of Business, told the VOA China may be trying to strike a balance between information control and government accountability.
"Since the party congress, we've seen increased measures, not lessened," Clark said. "So the big question ... is, when we get to the spring of next year, when the new leadership takes up the formal positions in the new government, is this the new normal?"