Name of connector that connects wires to washer drain pump
I'm afraid there's a good chance the connector could be proprietary or custom. Also, the connector housing and the two terminals inside are separate parts. Amana likely won't offer these in their parts catalog.

Amana might have bought that component from a connector manufacturer. The major players (Molex, Tyco, Hirose, etc) usually have their name or symbol somewhere on the parts they make, but if you can't find a recognizable mark, it's not likely to be a catalog item available through an electronic components distributor.

The connector looks fine; I don't see any signs of damage (discoloration, deformation, etc). I'd solder and heat-shrink the wire and resolve whatever damaged it in the first place.