Sign in to your Microsoft account at account.microsoft.com
Go to Your info
Select Edit account info
Add a new email address as an alias if needed
Verify the new email address
Set the new email as the primary alias
Remove the old email alias if you want it no longer linked
Sign out and sign back in on your Xbox with the updated Microsoft account email
If you only want to change the email shown on Xbox, update the Microsoft account alias, not the Xbox profile name