Anyone Know What this Connector is Called?

These parts most certainly are factory.
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Obviously it came from the bulkhead connector you are holding.
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That may be a '63 only bulkhead connector. The terminals at the red arrows are for the alternator output and the battery output/charge wires.
Having a big heavy connection like that provides more surface area and less resistance. Unfortunately if the screw or crimp is loose then its going to heat up when current is flowing through, just like any other poor connection. So looseness may have been a problem, but the question remains whether it was the cause. We'll discuss that next post.

If you can't get another connecytor, it sounds like you'll be OK with salvaging that one. Best thing to do will be to remove the all the of the male and female terminals from that side and the mating connectors. Clean or replace them. Get a new seal set from Detroit Muscle Technologies. Get a crimper some heat shrink tubing and good wire.
I'll edit this post with some links later on.