Ordinary Trainers cannot be battled again. In the Wild Area, there is a Trainer with all the starters' evolved forms that will battle you again and again. In the Battle Tower, you can rematch opponents, but who you get is random.
Champion Cup Rematches can be organized — allowing you to invite and re-fight all of the Gym Trainers. You’ll get more rewards for winning, and can fight unique new Gym Trainers like Marnie and Bede.
You can go back to Wyndon Stadium and challenge Gym Leaders or Leon. This is useful for leveling up your Pokemon and gaining money (you can get 10,000 currency from winning).
Sources: https://www.sportskeeda.com/esports/pokemon-sword-and-shield-things-to-do-post-game
https://bulbapedia.bulbagarden.net/wiki/Galarian_Star_Tournament
https://gameranx.com/features/id/188249/article/pokemon-sword-shield-everything-you-can-do-in-the-endgame-postgame-secrets-rewards-rematches/#:~:text=Champion Cup Rematches can be,Trainers like Marnie and Bede.
