They can make some general assumptions on you based on your ip address (that may or may not be a dhcp address or a box behind nat or a proxy), as well as the host mask generated by that ip (names of boxes and domains that your communication originates from....you see it alot in irc, etc).

If they recognize these they may assume it is you, sometimes this might even give away the country you come from (such as a person in australia having a host mask with a .au at the end).

Another way to realise it is you under a different name is you slipping up in your story, or your 'speaking style'. Many people have a default way of speaking in chat rooms or certain quirks that give them away no matter how hard they try to hide.

The information you give out to sign up for these rooms is only as secure as the companies who take it. Some will hide it all away, others might let it be browsed by anyone. At the very least every time you connect you might be giving out your ip address, host mask (which may reveal isp information, country of origin, part of the country you live in, etc), possibly the account you logged into your own computer with, etc. It all depends on your setup and the type of chat you are using.