Water cooler/beer tap valve cusp stem
This was a part that I couldn't find a precise name for, other than it being part of a cusp seat assembly for a water cooler/beer tap valve handle.
The bottom ring seats down into a gasket seal for the faucet, and the valve handle slides into the notched area at the top.
This particular tap was from a beer tube and seemed to be pretty generic. A lot of tap mechanisms seem to work in the same way but some customization may be needed to fit other tap handles. Hack away.