Ok, to change the username before the @ sign, that IS technically changing the entire alias, because a different username is technically a different email address.
What's your current domain address, is it outlook.com? If so, Can you sign into your personal account via this link: https://account.live.com?
If so, go to Your Info > Sign in preference, Add an alias.
Create new: this will allow you to use the native domain outlook.com to create a new alias. You can only create it if the desired username is not already taken by others.
Once you create this, you can make it primary alias and delete the old one.