I'm currently going through my vault, and I've noticed that a lot of my pet TC categories are for pets that I no longer own/have changed names/find the items better suit a new pet/etc, and it would be easier to organize if I could just change the category names, rather than creating a new one, moving all the items, and then deleting the old one.

Please, yes! I would also love to be able to change the order of categories!

Oou, I hadn't thought of that! An order change would be lovely, too.