BTW… If your Apple ID is linked to something other than an iCloud Mail keep in mind that you won’t be able to switch to an iCloud mail address as primary address for your Apple ID. I did all this transition last week and spoke to apple for like an hour. They told me there is no way to switch. So now my gmail is like the user name for my Apple ID, every mail that is sent to gmail now gets forwarded to an hide my mail email.
The problem was, that „hide my mail“ mails get normally forwarded to your primary Apple ID Mail address, in my case the gmail address. So what I did now was creating an iCloud mail over my iPhone‘s iCloud settings and then went to iCloud.com on my browser, where you then are able to switch the „hide my mails“ recipient address to the just created iCloud mail. Pretty complicated solution, but the only way to at least kind of get rid of my gmail address…
I already changed about a dozen services from my gmail address to my @me address, but I have a ton more I need to track down
I also set gmail to forward all emails to my @me address so I can monitor stragglers since I anticipate I will be getting emails to gmail for a while still