What is the name or part number for the female.

That plug is part of a huge wiring harness and is only replaced if it has a problem while the car is under warranty. The harnesses are repaired when it's out of warranty.

If you see blackened terminals, you will also find that two of the wires are hardened for about the first four inches from being overheated. Solder will not flow and adhere properly to the hardened part. Replace the switch. If you try to reuse it, the contacts inside will just continue arcing and overheating and will make your repair ineffective. Remove the blackened terminals from the connector body and replace them individually. Most likely the plastic connector body will be melted too. Just cut those parts away. Use two appropriate-sized crimp-type terminals, but solder them too to 4" of new wire of the same gauge. Cut off the hardened parts of the old wires, splice the new wires to them, and seal those joints with heat-shrink tubing.