Please review these several steps to insure your anonymity on IRC.
Your last name is visible to others.
Please look at File>Options by either choosing the command or clicking on the Options icon:
or 
In the resulting dialogue box, if there is a '+' to the left of words 'Connect' and 'IRC' click on the '+' to expand those submenus:
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But notice that the field called 'Full name:' is greyed out and cannot be changed if you are connected. You will need to disconnect briefly to be able to edit that field. First let's check a few other fields while we are in mIRC Options.
Click on 'Identd' to see that page in options:
In the 'User ID:' field, put something short, simple and anonymous like just your first name.
Click on 'Messages' to see that page in options:
In the 'Ctcp finger reply' field, leave it blank (or optionally put something short, simple and anonymous like just your first name).
Click on the <OK> button to close the dialogue box.
Now we will correct the 'Fullname:' and 'Email Address:' fields in the 'Connect' Option. To do this, you must disconnect without quitting mIRC. Either use the File>Disconnect command or click on the Disconnect icon:
or 
Now open File>Options by either choosing the command or clicking on the Options icon:
or In Options, click on 'Connect' to once more get to this screen:
For 'Full Name:' put something short, simple and anonymous like just your first name (or even the word 'Anonymous').
For 'Email Address:' put something anonymous like 'askme@myisp' or anything else fictious.
Click on the <OK> button to close the dialogue box.
Reconnect by using the File>Connect command or click on the Connect icon:
or 
The mIRC program will remember these changes in the future, so you are done. Thank you for taking the time to review this.