I just spent an hour troubleshooting this issue for my father's account. He has been using his
@me.com email address and we just updated his computer's OS to Mojave.
He has three email/domain options that can be used for this apple id: @mac.com @icloud.com and
@me.com. I noticed on his Mac that it had his apple id labeled using the @mac.com domain, which is incorrect. So, on a whim, I decided to log into his appleid account using Safari and check the settings. Sure enough, the @mac.com address was checked (I was able to send emails using that email)
By selecting his
@me.com address as the account name for his apple id, his emails started sending again using the
@me.com address.
So, if you're trying to use an @icloud.com domain, just login to appleid.com and select the @icloud.com as your apple id.