Well, I had some success at putting a name to it (or close enough) - it seems to be a "tilting breast plate with mentonniere " which I assume means a chin guard.
It's a Wrapper. And it is an add on piece of armor that would be worn over the armet and bevor. Since the encranche or targe is mounted on the left that is a target for the lance, the wrapper adds a level of protection in case of a miss or the lance runs up off of the encranche. It serves to help deflect the lance. Most are full and look like an extra bevor but are separate from the helmet. The one in the photo is a bit of artistic license and essentially useless with the perforations in it and free floating like that.
I have always hear it referred to as a Buff. Typically it was worn in conjunction with a grand guard. That is what the troop I worked with called them.
Here are some modern examples (see the pics towards the bottom of the page):