I did see that, @bakman2 , and thanks for the tip -- I can see that that will work. In a practical sense, I don't really have full access to Home Assistant's containers, and creating a new one would take more time and computational resources than I'm willing to put in for such a small bit of information (I'm not particularly facile with Docker). Mostly right now I want to know if HA exposes that information somewhere...if not, I'll stop looking 
For the time being, my workaround is just to hard-code the hostname and graft it onto all outgoing MQTT requests -- took all of two minutes to put into place. That will tide me over until there's a more "official" solution.
