Problems with having two emails

Hi,

I'm having some trouble with my mum's email. She appears to have two primary email accounts, one of which appears to be completely out of control and is causing issues sending messages (as well as having the wrong name).

The one she uses is @me.com whilst the (what appears to be an) alias uses the same email with @icloud.com. I cannot delete it like an alias (there is no minus button). I cannot delete it on 'reachable at' on the Apple ID settings. It's causing many issues and I don't know why it exists (we certainly didn't set it up).

Any help would be appreciated :)