Is there a keyboard shortcut to open the filename popover menu in Preview, Pages, etc.? I'm referring to the popover menu that opens when clicking the little down arrow next to the file name in some apps.

I use that extensively—it would be convenient if there were a keyboard shortcut to open it, but I haven't found one yet.
I don't know of one, but you can of course use Command I (Get Info) in the Finder to change the name or assign Tags.