Anyone Know What this Connector is Called?

Yes, two of my A's have those, and my C-body. I term them "bulkhead buss-bars", used to feed-thru the high ALT and BAT wires. They were used only in 1963 and 1965. I like them so much that I bought the cabin harness for a 1965 Fury off ebay ($30) to install the bulkhead in my 1964 Valiant, to match my 1965 Dart and 1965 Newport. I had to cut the firewall hole 1/8" taller to fit. Other years ran those high currents thru the more regular Packard terminals (spade) in the bulkhead, which causes continual problems with overheating from corrosion and melting. Some years have bigger Packard terminals, but still doesn't work well since a slide fit, instead of bolted like yours. A 1965 bulkhead would give you more terminals for future wires, but might be slightly taller. Around 1966, the bulkhead got 3 connectors when they moved the wiper motor to the engine bay.

I don't know why you can't re-use yours. They are tin-coated copper so you can easily beat flat with a hammer. Yours look a bit flimsier than my 1965, where the cabin wire slides into a cylindrical housing and was welded or soldered. Clean it well, crimp, then solder. Solder protects from corrosion. On the engine side, you can use any new wire you want under the bolt. Your wire looks fine, so just add a little solder to the crimp. The factory wire was 12 awg, but I used thicker 8 awg (or 6 forget).

You also need to find why you had either excessive current or heat from corrosion. Did you install a higher output alternator? Check that the ammeter wires on the dash cluster are properly insulated from ground. Since only the BAT+ terminal on the ammeter was burnt, and that bulkhead buss-bar, it sounds like that wire became grounded at the ammeter. Perhaps the ammeter needle assembly fell apart internally. One common corrosion source is a "welded" connection where a bunch of black ALT wires are fused and wrapped with friction tape. That often becomes green with corrosion under the tape. I kept those wires fused together, cleaned the outside as best I could, and added solder. But, that would make heat on the black ALT wire, which you don't see, but still check it to avoid future problems while "in there".

In my cars, I ran an alternator bypass wire in the engine bay to keep excessive current from routing thru the cabin. I used parallel-reversed diodes so that normal flow is thru the ammeter, until the diodes start conducting more in forward-bias (>0.5 A) to shunt current direct to BATT+. That keeps my ammeter working, without pegging it with a higher output alternator. Search for my post on "modernized wiring" if interested.