Use of iCloud.com address from Mail app

Hi,

My  ID is a gmail.com address. I have created an iCloud address on iCloud.com, at least I believe it’s an actual address, and not some alias. I picked the name etc., and I am able to use it from iCloud.com. However, I would like to send emails from the Mail app. It however does offer me only my two Gmail accounts, and to hide my email, in the dropdown menu From, when I’m choosing from which account I’d like to send it.

I have entered the “new iCloud account” under accounts, in Settings > Mail. I entered my  ID pass for the iCloud account, it seemed it’s done, no error message.

However, not able to use the iCloud.com mail to send messages, and also apparently not to receive messages, one test message arrived in the Mail app, but nothing else since.

There are tons of similar threads, but am not able to go through all of them to find out if someone has the exact same issue as I do.

Any sort of assistance would be appreciated.

Thanks in advance.