If you are connected to a network, you can use /fullname <name>
If you aren't connected to a network, go to mIRC Options, Connect, and change what is in the full name location
With the exception of the information entered for your registration, this is the only place in the mIRC program where your real name shows up. And as far as the registration goes, that information is stored on your computer, and is inaccessable to others.
