Without knowing the network involved, i cant say for sure since each has their own ways of doing this. For example, on DALnet, what you would do is use the command including the password of your choice (passwd isnt a good choice, use something not easily guessed) and you would then get an email to complete the registration by using an authorization number in a command you see in the email. When you identify to that nick, using something like /identify thepasswordhere you have to be sure you use it exactly as you did in the command. CHICKEN isnt the same as chicken or cHiCkEn. Its likely that if an auth code is needed to complete the registration and you dont do that, the nick will drop in a certain period of time.

If you dont see help channels listed in the MOTD(Message of the DAY, all the stuff you see scroll by when you connect), see if there is a #mIRC on the network you are on ( just type /join #mIRC) and ask what channel you can go to for help with a nick registration problem.