I assume you have your belly button pierced.
No, you should never clean your piercing with soap, especially scented soap. It gets in the way of how your body heals, and causes tons if irritation.
Just do sea sat soaks. Get a premade bottle of saline solution, you can get this at any drugstore, and use that to clean your piercing.
If you do not have a piercing and just cleaned your belly button with dish soap, then it shouldn't cause any issues or weird reactions.