Once you are logged in, you will then need to register your email by "editing your profile" - see screenshot:
Once you are on your profile page, enter an email in the appropriate section on this page. Once you've entered an email and clicked "save" at the bottom of the page, you will receive an email from Rise, asking you to verify your email.
Once this is done, log out from Rise and then log back into Rise using the email login process. If you've never logged in using email before, you will need to click on the "Forgot your password" link and request a new password. See screenshot:
Once you've received a new password from Rise, then login to Rise using the email login process.
Go to "Edit Profile", and navigate to the "Connected Networks" section of your profile. Unlink your Twitter network, and then re-connect using your new Twitter handle. This will then update your profile details on all the boards you are playing on.