Accessing @icloud.com email when you use your @me.com email address as your ID.

In the discussion you wrote -

My Apple ID does not include "@icloud.com." My Apple ID is "example1@me.com." - this Apple ID is signed in Mac system preferences and is a primary mail address .

I have to use that ID to login .Once I am in , there is no reference to my "example2@icloud.com" address . On my Apple email , I do see both email addresses and can receive and send emails from either.

If the Apple ID is signed out from system preferences > and a new Apple ID is created say example1@icloud.com and set up the two mail address will be active in internet accounts and again you sign in with same Apple ID say example1@me.com in system preferences the primary Apple ID is set up .

You can add the newly created Apple ID with iCloud domain that is example2@icloud.com in internet accounts https://support.apple.com/en-au/guide/mac-help/mh35565/mac

https://support.apple.com/guide/mac-help/add-an-internet-account-mh43559/mac

jegrijalva wrote:

While I receive email on the @icloud.com account, I am unable to access it to change the password or to make any other changes.

I am not following what you mean by "I am unable to access it"? Can't you use your @iCloud Apple ID to login to https://appleid.apple.com?