When named mobs are killed, I see the entry in the game chat, but the same information is not captured in the log, nor does it get sent through my Discord Integration (which does capture player deaths). Is there something wrong with my configuration or something I can do which will log/send named mob death entries?

The message is sent direcly to players, much like how it's done to pet wolf, cat, or parrots, just that it is sent to all players and I assume those messages aren't sent to the Discord hook. I'll look into this.