Hi. I'm Brian and I'll try to help.
This forum is dedicated to problems using Outlook for Mac. Issues with your Microsoft account are handled in a different forum.
The best way to change addresses is to log into https://account.live.com/names/manage and add a new @outlook.com alias, then give that alias out to people. Email sent to either address will arrive in your Inbox because both addresses are for the same mailbox. At some point in the future if you wish to eliminate the old address, make the new address the primary alias (which you can do at any time if you wish) and then delete the original. That deletion is immediate and permanent. My preference is to keep the original alias. You'll still get email sent to the old address in case there's someone who has it and you've forgotten to update them.
What you can also do, but it's not as optimal, is create a new account and access them both, but you'll need to use a mail client (like Outlook for Mac) if you wish to move data from the original account to the new one. Using aliases means that no mail needs to move.