We are working on getting users the ability to change the email addresses associated with their SmartThings accounts through the mobile app itself.
For now, please contact support from the address you currently use to access the SmartThings app, and we'll get it sorted out for you.
If you recently signed up for SmartThings with a Samsung account, you can change your Samsung account ID either by navigating to your Samsung account profile in your Samsung mobile device's native settings (steps vary by device) or by logging in to your Samsung account here and clicking My Account Info > Change email.
IMPORTANT: Note that any Samsung service using your Samsung account login credentials will be impacted if you change your Samsung account email address. You may need to log back in to these services with your new account ID.