How can I delete/turn off an @icloud.com address?

Hi Dominik G,

welcome to this Apple (user-to-user) Community!

Apologies that no-one has, as yet, replied to your questions. Am doing what I can to help, using Apple support's documentation (links below). ie: aiming to share the way Apple has things set up to work.

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Re: "How can I delete/turn off an @icloud.com address?"

As far as I know, (am no expert in this area) the primary email address can not be delted.

Seems that primary address is necessary, as we can't sign in to iCloud.com with an email alias.

Apple Support's online article: Create a primary email address for iCloud Mail - Apple Support

Eg: says:

"After you set up your @icloud.com email address, you can use it to sign in to iCloud.com and your devices in addition to your Apple Account. See Use your Apple Account with iCloud.

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Re: "Also, in account.apple.com it shows, that the @icloud.com email address is an alias of my Apple Account primary email address. Is there any way to delete the @icloud.com mail or deactivate it?"

The primary and the alias email addresses all end in @icloud,com

Our iCloud email aliases can be deleted.

Add and manage email aliases for iCloud Mail on iCloud.com - Apple Support

Eg: says:

:Turn off, turn on or delete an alias

You can turn an email alias on or off at any time. You can also delete email aliases that you no longer want to use. Turning off an email alias is temporary; deleting it is permanent. When an alias is turned off or deleted, email sent to that alias is returned to the sender.

1. Go to icloud.com/mail, then sign in to your (if necessary).Apple Account
2. Click at the top of the Mailboxes list, then choose Settings.
3. Click Account, select an iCloud Mail alias in the list, then do any of the following:

• • Turn off an alias: Select “Disable alias,” then click Save Changes.
  • Turn on an alias: Deselect “Disable alias,” then click Save Changes.
• Delete an alias: Click “Delete alias,” then click Delete.

• • Note: If you have three email aliases and you delete one, you must wait 7 days before you can create a new one.
  • Note: You can’t use an alias to create a separate Apple Account."

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Re: "... now, I own a website domain, so I used the iCloud+ feature of creating free email address with that domain. And now I am trying to get access to only that email address without also having the first @icloud.com showed up in the app"

See how to: Set up an existing domain with iCloud Mail - Apple Support

and

Use Custom Email Domain with iCloud Mail - Apple Support

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If more help is needed:

You can contact iCloud Support: (There is a "Get Support" link (online chat, phone, eMail etc) at the bottom of their website (link below):

iCloud - Official Apple Support

All the best :-)