There are a few ways a person could find your IM name...

1. You inadvertently signed up in the IM service's public database, so others can do a search and find you. It may be labeled different things depending on the service. Usually you can find the link in the IM client somewhere to access, modify, and/or delete the information. It would probably be advisable to remove your information or, if required, keep it simple, so others would have a hard time finding you. Spammers can crawl the web and grab your screenname from the database as well.

2. On a third party site, especially a message board or bulletin board service, you entered your IM name when you registered, so others participating on the message board can chat with you one on one. Usually the IM name is optional. Just edit your preferences and delete the IM name you entered. Spammers can crawl the web and grab your screenname from the message board as well.

3. A spammer uses a computer program to generate a list of IM names based on dictionary words and common proper names. Then the spammer sends an unsolicited offer to all of them knowing that some of the names have not been registered or are not online. There is not a lot you can do in this case. Do not respond to the message. Warning or blocking the person will usually get the attention of the IM provider because others will be doing the same. You may also contact the provider directly. Unfortunately, the spammer will probably just register under a different screen name and continue spamming.

Some services notify you or ask for permission before allowing another person to add your screen name to their buddy list. AIM does not, and I'm not sure about the others. Usually you can block an offending person from contacting you again some where in the preferences. I use Gaim, which allows you to login to multiple services, and you can just press the warn or block button on the chat window to do so.