This isn't obvious to everybody.
When you edit your profile, you look under the Identity sections, and there is "Email Address". Beside email address, you see
Changing this does not change the e-mail address you use to sign-in
Not everybody heeds the warning there, and this is where a lot of confusion starts.
If you enter a new email address in that box, all that you get is an account with a second email address. Not an account with a changed name, or even with a changed email address. And not an account with a secondary GMail address, either. If you enter a GMail email address, you should (though may not) see
You are not allowed to have a GMail address as the primary address for your Blogger account.If you want a different GMail address, you setup a new Blogger account, and you transfer your blog(s) to the new account. Alternatively, setup a new non GMail email account, and change the existing Blogger account to use the new email address for password recovery.
And need I state this again, when you need to change your email address, do this before you forget the password to the account with the current email address.