Their nickname and a few fun things, such as their favorite color or rock band, will suffice. Instant messages or private messages of any kind should be monitored carefully. Chat room moderators can't see what's going on in private conversations and won't notice if your child is getting into a dangerous situation. Encourage your child to stay in the chat room with all the other kids instead of allowing them to be pulled aside and spoken with privately. Though it may seem flattering, it can be unsafe.
Some people use private messages to send porn pictures or sexual content to children.
Discourage your child from accepting private messages. These files can be sent via private message. Teach your child not to accept any files, and if they do accidentally receive one, never to open it. Should your child accept a file like this, delete it unopened and inform the room moderator or channel operator. Be aware that new viruses are being developed all the time and some of them contain what are usually considered to be safe extensions.