OneSoulLegion created this issue Nov 20, 2016
I believe I mentioned this before in a comment on the page, many months ago, but I figure making a proper CF ticket for it would help you keep track of it for future consideration.
Currently, the way the system for companion profiles is set up means that they are global to your account. It would be very useful to be able to have such profiles be character specific, or togglable. That way, the flying machine my goblin engineer built and the one my dwarven engineer built do not need to share a profile and look identical (for example).
One way to implement this might be to be able to "toggle" companion profiles on or off on individual characters (the "toggle list" being saved on a per-character basis, even if all profiles are visible for all characters). Naturally, the addon would have to warn you if you had more than one active profile connected to the same companion (or in some other way solve this conflict).

We have discussed this internally and decided to go for making every companions bindings stored at a character profile level (not simply character, meaning two characters using the same profile will still have the same bindings) as the other (current) way is the less likely behavior (and you can still bound a companion to the same profile manually if you need to).
This way we will avoid adding complexity to the UI and just change the behavior to meet the general user expectation.
This will also solve the issue with mage's water elemental and similar non-named pets.

No ETA for this change, but I would like to have it in the next update.