Microsoft has made it easier for users to rename their accounts which is used with Outlook.com, SkyDrive, Windows 8, Office, Windows Phone, Xbox, and other Microsoft services.
Several years ago Microsoft launched the ability to rename or to add aliases to your account, which gave important flexibility to manage these changes. In April, the company added the ability to sign in with any alias on your account. At that time, Rename was left unchanged; and it walked you through an experience to add a new alias and switch which one was the "primary" alias on your account.
Today, Microsoft replaced renaming with a simpler and clearer choice to make any of your aliases a primary alias. The company has also made it clearer why you might want to do this (and why you might not). Now that you can sign in with any alias, really the only reason to make a different alias your primary one is if you want a different email name to show on your Microsoft devices, like the background of your Xbox or your Windows 8 PC.
To manage your aliases (or make other changes to your account), go to https://account.live.com/, click on "Account aliases" in the left navigation bar, and then follow the instructions.