I'm another customer and I was having the same problem Fax22.
Last week I was finally migrated from Outlook.com to Outlook Mail (that is to say, from the recent to the new version of Hotmail).
1. In Outlook 2016 I went into File > Info > Account Settings and the account still showed as the old kind.
2. I deleted my Outlook.com account.
3. I closed down Outlook 2016 and signed-off Windows.
4. I logged back on and re-started Windows.
In Outlook 2016 I went into File > Info > Account Settings and added back my Outlook.com account.
5. The account type is now simply 'Microsoft Exchange'.
6. After waiting several minutes for the email to be re-synched I logged off Windows again.
7. I logged back on to Windows.
8. I restarted Outlook > New Email.
9. The aliases now appear as options when I click the down arrow by the Sender box and I can send email using an alias.
For me, at least, removing and adding back the Outlook account so the account type is simply 'Microsoft Exchange' solved the issue of sending email with an Outlook alias.
(I'm running Outlook 2016 (from Office 365) on Windows 10 RS1 64-bit, both with all the standard Windows Update updates. And I use Kaspersky Total Security 2017.)