It's common to have some item of clothing with one's sign on it in the castle, but it's up to individual choice. There are enough high-ranking mages there that can sense your sign near-instantly that there's no point in hiding it, and people have fun incorporating it into their outfits.

People who are visiting other nations or going to battle will not have anything with their sign on it in order to make it more difficult for low-ranking mages to empower their spells with the appropriate cards.