Actually, if you want, you can create an entire new icloud.com email address rather than an alias. I was stumped on how to do it but I finally figured it out! This is if you already use apple mail program on your Mac or iDevice. I have found NO other way online and no answers in any thread.
Here are the steps...
1) Go into Mail system preferences either by (Apple menu, preferences, Mail) or via the Mail app.
2) Click the + button as if adding an existing email account.
3) Chose iCloud and hit continue.
4) Hit "Create Apple ID..."
5) Enter your locations and DOB and then hit "Next"
6) Chose "Get a free iCloud email address" and then fill in the questions... It will tell you if the name you want is taken or not. (p.s, I unclick "Email Updates" as I already get those on my other account.
The rest is pretty self explanatory (but I will show just in case) 🙂
7) provide the security questions and enter Rescue email - I used my other apple email address
8) Click the box to agree to terms and BOOM... you got a new apple email address. Unfortunately, there is no way to get a @me or @mac account... however, you can give out your new email address using @me.com instead of @icloud.com and it will work too 🙂
HOPE THIS HELPS ANYONE LOOKING FOR THIS INFO LIKE I WAS!!!