You mean, like, have the player playing the game have the ability to enter his or her own name for the characters in a party?
You need to select the command (in the event editor) "Enter Hero Name", then select the character you wish for the player to enter his or her name and that's it!
To have NPC's / Cutscnes mention the name, you need to put in a n[0] code in the text boxes (the number represents the hero in the database), and make sure your using version 1.05 (or higher), because some of the earlier versions of rm2k3 don't allow the enter hero name to work.
EDIT: I forget if it's h[0] and something else you need to put in for this to work, considering it has been awhile since I've used the default text box...but I think that's it...