Proper name for this bit?

It's similar to a Tom Thumb - except for the rings at the bit level, (which I'd assume will allow for double reins). It is not a snaffle. It's a shank (leverage) bit and is a very strong bit. Once a shank bit has a joint in the mouthpiece, it becomes potentially quite severe. True snaffles have only a place for attachment of reins directly at the level of the mouth piece and can have 2, one or no joints (mullen mouth). A shank bit with a straight or ported mouthpiece is much more kind to a horse's mouth.