Prior to June 2013 you could link existing Microsoft accounts together. To increase your security, we’ve retired that feature so it's no longer possible to link a Microsoft account (even with separate email addresses) or a non-Microsoft account (such as a Gmail account) to an existing Microsoft account.
If you want to change how you sign-in or how your name appears to people, you can add an alias to your existing Microsoft account. This alias acts as a nickname for your account and uses the same inbox, contact list, and account settings. For more detailed information about how to add an alias, including why and how to set your primary alias, see the Manage aliases on your Microsoft account article.