<p>Whenever I use the signal/slot editor dialog box, I have to choose from the existing list of slots. So the question is how do I create a custom named slot?</p>

Unfortunately this is not possible in Qt4.
In Qt3 you could create custom slots which where then implemented in the ui.h file. However, Qt4 does not use this file so custom slots are not supported.
There is some discussion of this issue over on
QtForum