Rename iCloud mail?

So I just recently underwent a name change (including a surname change) from 'Michael' to 'Ian'. My iCloud mail was set up under the Michael name & I want that removed so my family cannot reach me. Apple says this is impossible when I call them. Is there a way to do this or delete my iCloud mail without deleting my entire iCloud account?

I understand aliases and am using one currently, but I wish to remove the Cloud IMAP account (or rename it) so it's out of the equation for issues with contact from my old life.