Anyone Know What this Connector is Called?

Lets try to figure out what went wrong.
This will require getting you up on how the electrical system is set up.
The wires from the battery positive to the 'alternator' gage continue on to a welded junction.
At this junction the alternator positive joins the battery positive and feeds going to the various main circuits.
View attachment 1715690229
When the engine is running and the alternator working, power flows from the alternator to the main junction and then to where ever needed.
If the battery needs recharging, current flows to the battery. The ammeter needle moves toward charge.
If the alternator can't supply the power, then the battery does. Current flow out of the battery and the ammeter shows discharge.
Normally right of starting you might see the needle move as much as halfway toward Charge (20 amps) then move to zero over the next few minutes.

So if you can recall what the situation was when the wires were heating, and what the ammeter was showing, there may be some clues as to what went wrong.
The best that I can remember leading up to this the gauge was wobbling more to the right toward charge. When accelerating it would drop slightly but was pretty consistently pointing in the charge direction.