My project is heavy on smart shapes and I am using a plethora of styles. Is there any way to organize the styles names when they display in the Style Name drop-down box on the Properties panel? It does not seem like there is but I thought I would ask.
Not AFAIK. Contrary to captions, where you have a whole bunch of possible Default styles, this is a lot more limited for shapes. I have already logged several feature requests to have this changed. When you know that a shape can be used both as a text container and as a button this is really necessary. Since shapes appeared with CP6 I alsos prefer shapes over any other item.
Another problem is the fact that you don't have a hierarchy. If there were text styles which can be used both in different shapes and shape buttons the situation would change. The new Copy/Paste Appearance makes it possible to copy only the text style, and I use it only for that reason, never to replace an object style.
Cannot help you more. Trying to limit the styles, using the default styles if possible. It would also help if you could use the styles of the Quizzing category for other purposes, but that is impossible as well.