1. Log on to Outlook.com with your current alias/email address. For example email@example.com
2. In the upper right corner click on your display name, and from the resulting drop down menu, choose “Account Settings”.
3. This will open in another window, and may require you to go through a security confirmation exercise. I had to receive enter in a code that was sent to me via txt.
4. Once verified, in the menu on the left of the screen, click on “Aliases”.
5. Click on the “Add alias” link.
6. Put in the new alias you want to use, note that you can change the domain name to/from the localized domain. In my case I went from outlook.co.nz to outlook.com. (I found that some Azure management tools didn’t like me trying to log on using the localized domain.). Click on the “Add alias” button.
7. Once the alias has been committed, you can click on the appropriate links to make the new alias the primary alias if you so desire. You can also remove the old alias. According to Microsoft, you should be able to use either alias at any time, interchangeably. I haven’t tested this, so mileage may vary.