What is this bracket called

Remember that the rocker panel and its extension that you are talking about is actually a "box beam", though it isn't square, that is part of the "frame" of the original car so tying it to the front subframe is really important. Those two side to side pieces tie two parts of the "frame" together. If you go with a beefy subframe connector like that runs right to the front subframe (like OldManMopar did), the "rocker beam" is less critical, though still important. The big holes drilled in those pieces don't help you (I don't know why they are there) and you might consider welding patches over them if not needed.