Tor can’t solve all anonymity problems. It focuses only on protecting the transport of data. You need to use protocol-specific support software if you don’t want the sites you visit to see your identifying information. For example, you can use the Tor Browser Bundle while browsing the web to withhold some information about your computer’s configuration.
Also, to protect your anonymity, be smart. Don’t provide your name or other revealing information in web forms. Be aware that, like all anonymizing networks that are fast enough for web browsing, Tor does not provide protection against end-to-end timing attacks: If your attacker can watch the traffic coming out of your computer, and also the traffic arriving at your chosen destination, he can use statistical analysis to discover that they are part of the same circuit.