After some "research" into this, I have personally settled on `amenity=dressing_room`.
First, it is the only tag I could find with a wiki page at https://wiki.openstreetmap.org/wiki/Tag:amenity%3Ddressing_room .
Second, from all the tags I could find it has the highest use. While not by a very high absolute margin, given the small overall number of such features mapped, that is also a good indicator.
* amenity=dressing_room 128
* amenity=changing_room 42
* amenity=changing_rooms 4
* amenity=change_room 1
* amenity=changing_cubicle 1
* amenity=changing_booth appears 0
* amenity=change_booth 0