Is it possible to export a list of images that includes the name(s) of any collections that include them? A text export would be fine except that I cannot find a variable for the collection name.
No, not currently. Though I'm not sure I understand what you're requesting? You would select some set of images anywhere in Photo Mechanic Plus (folder-based contact sheet, search-based contact sheet, browse-based contact sheet, etc.) and then choose this export command and it would (for each image) list the Collection paths that they each belong? And this would go to a text file? Am I correct in my understanding?
I suggest making a Feature Request.
-Kirk