In an interview Mr Schmidt said he believed that every young person will one day be allowed to change their name to distance themselves from embarrasssing photographs and material stored on their friends' social media sites.
The 55-year-old also predicted that in the future, Google will know so much about its users that the search engine will be able to help them plan their lives.
Using profiles of it customers and tracking their locations through their smart phones, it will be able to provide live updates on their surroundings and inform them of tasks they need to do.
"We're trying to figure out what the future of search is," Mr Schmidt said. “One idea is that more and more searches are done on your behalf without you needing to type.
"I actually think most people don't want Google to answer their questions. They want Google to tell them what they should be doing next."
He suggested, as an example, that because Google would know “roughly who you are, roughly what you care about, roughly who your friends are”, it could remind users what groceries they needed to buy when passing a shop.
The comments are not the first time Mr Schmidt has courted controversy over the wealth of personal information people reveal on the internet. Last year, he notoriously remarked: “If you have something that you don’t want anyone to know, maybe you shouldn't be doing it in the first place."
Earlier this year, Google was condemned by the privacy watchdogs of 10 countries for showing a “disappointing disregard” for safeguarding private information of its users.
In a letter to Mr Schmidt, Britain's Information Commissioner Chris Graham joined his counterparts in countries including Canada, France, Germany and Italy, in raising concerns over its Street View and Buzz social networking services.
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