I'm having a very similar issue. I am logged into iCloud Mail on the icloud.com website from my Mac. I have tried numerous times clicking on the gear icon> Preferences> Accounts> "Add an alias", and have tried entering various alias address names never getting any indication if the name is already taken. I have 2 of 3 aliases being used.
Taken names should show up in red asking to come up with something else, but it never does. All that happens after clicking "Add" on the bottom right of the window is the window quickly "blinking", and back to the "Add an alias" window.