When an event as been split into two events, is it possible to rename the individual events? It can’t find a way of doing this. Highlighting an event and editing the name above the Inspector applies the new name to all previously attached events. It works OK if events on a track were not split and were just recorded individually. I assume it’s something to do with there being one clip referring to both events as coming from the same WAV file. Perhaps there’s a way of splitting the clip to create and to point to two separate WAV files?
If you really want to do this you could follow the procedure listed on page 195 in the CB Pro 9/Artist 9 manual titled “Creating New Files From Events”. You would have to perform the mentioned “Bounce then choose Replace” procedure described in the manual for each event. Then, rename each of them to what you want.
To me, this seems like a lot of work but, I’m sure you have your reasons. Good luck 
Regards 
As Prock said, that bouncing procedure will do it, however, you may also want to consider just coloring the sections using the Range Tool. The bounce selection is not too much work for me but it can be tricky. You can rename files in your media pool. You can also create Regions and then create new tracks from the Regions. When you start cutting up files with the Audio part editor things can get a bit tricky for sure. Good luck and keep working with it.