This is something that would appeal to roleplay groups. Could you open up API access to allow the companion costume and the companion mount settings to be changed. If this is not possible, could you add another option in the existing companion settings (where it shows "Default Mount") something like "Match Mounts" and "Match Costumes"?
Thanks for considering this. I know it is not as easy as it sounds.
Changing your companion's mount/costume is already available to the API. You just can't do it outside of the interaction. So it will not be possible for anyone to make an addon that will change the companion's costume for instance while you're walking around or when your own player costume changes. But an addon can be made to auto change the companion's costume based on any kind of criteria once you open the Companion menu.