It is possible to change both your main user profile email, which is used for logging in, as well as the email that is visible publicly to other users if you have a Public Repository.
Changing Your Login Email
Step 1 - Login as the Admin User that Created the Account
Step 2 - Select the User Icon on Top Right
Step 3 - Select to View Full Profile
Step 4 - Select Edit Name and Email
Step 5 - Edit the Email to Your New Email and Select Submit
Step 6 - Verify New Email
Verify the new email for the account
You will receive an email to your previous account email in case you made a mistake
The account will display "Waiting for Verification" until you confirm your new email.
Step 7 - Login with Your New Email
Changing Your Public Facing Email
This email shows to other users when they are viewing your account. For example when linked from a public repository.
Step 1 - Select the (...) Menu in Your Account
Step 2 - Edit Your Email