You can change it by dragging your person to the clothes at the corner of your screen when you're visiting a villager's home, but you can't change it when you're designing a home or in the dressing room before leaving Nook's Homes; it'll only let you change your accessories, socks, shoes, hats and skirt/pants.
oh, i don't even remember that -_-;I wish you could atleast pick a colour too. You start the game in that grey blazer for about 20 seconds and I think that looked much better.