Registering a nickname has nothing to do with mIRC. It's a service provided by some individual networks. You register a new nickname in the same way you registered your first one (either with NickServ, which is the most common, or whatever other network service exists). Just change over to your new nickname and do what you did before.
To the best of my knowledge you cannot transfer old settings to a new nickname, or transfer "registration" to a new nickname. You have to start afresh.