I don’t put chapter numbers in my chapter names (folders). But I often wish I could see the chapters numbered, which would greatly help in my reference materials and knowing where things are as I write.
Is there a way to see what number a chapter is, or have it numbered, without it exporting as part of the chapter name?
You can toggle a hierarchal numbering in the outliner view. 
Ah, great. I wish it were in the binder itself, but this can work. Thank you!
You can also enable numbers in the Corkboard view.
If you don’t use the Synopsis at Chapter level, you could place the title in there and read in the title from there instead of from the Binder. I read in my time and venue changes this way when compiling. I summarise my synopsis at Scene level, so there’s never a clash.
If that doesn’t work for you, you could create a metadata field for Chapter Titles and read it in with a placeholder. The thing with placeholders, there must always be underlying data, else compiling leaves a blank space. But you’d never experience that as each chapter has a title — and if it doesn’t, you’ll know you forgot to add the particular one(s) to the chapter title data field.
In both cases, you’d have Chapter number and title in the Binder — and plenty of redundancy (repeated titles to manage) — but read in the title alone from one of the options at output.
The drawback is if you move Chapter 24 to Chapter 76, you’ll have a whole lot of manual renumbering to do in the Binder.