Is there a rating of the 3D-ness of a 3D movie?

There doesn't appear to be any official rating system, disappointingly. As a previous user @Pubby answered, what you are referring to is the "depth" of the film (as per Wikipedia):

Depth perception is the visual ability to perceive the world in three dimensions (3D) and the distance of an object.

A few websites have had users try and champion a ratings system (e.g. Meant to be Seen), but nothing has been adopted by a "large" company. The nearest thing to a decent ratings system I have seen is a blog called 3D Perfection, where the author defined his own 3D ratings system as follows:

3D....Perfect use of 3D. There is an excellent 3D depth throughout the movie and several pop-out moments.

2.9D....the 3D depth is very good and consistent throughout but occasionally there are anomalies. This could be some scenes that lack a 3D depth or a few scenes that are incorrectly aligned etc. (overall though, there is nothing too distracting to really spoil the vast majority of the 3D)

2.8D.....a mixed bag of both strong and weak 3D. There are several scenes with nice 3D depth but unfortunately there is also a large amount of moments with weak 3D (a narrow separation or even incorrect alignment)

2.7D....generally weak 3D with a narrow separation but occasionally a good 3D scene might pop up.

2.6D.....poor 3D. There is a very narrow separation and the 3D effect is weak and flat looking.

2.5D.....a poor post production conversion.

He's rated some 95 films on his blog in this way. It's not much, but it's better than anything else I've come across.

The term would be depth (or rather, the illusion of depth), although I haven't seen any actual ratings of it.

Films that really seem to pop are generally filmed in 3D and then enhanced post-production when adding in special effects.