I personally would call it a hot shoe to plate mount adapter. Don't know if there is a name for it, really. And, I'm not a photographer, smeer was the one who knew about these things.
It appears that it is basically a single-jointed articulating arm with a hot shoe mount on one end and a generic plate with holes on the other. Maybe you could find something similar and just drill the holes in the correct position yourself.
That one looks like it'll be easier to find replacement mounts if you need to in the future. Looks like that standard photography screw tripod mount thingy. (Again, not a photographer :crackup