From your current Hotmail account, you can make an alias and set this alias as your 'primary alias':
If you want a new name for your account, you can add an alias, make the new alias primary, then remove the original alias. Source
a) To add (or remove) the alias:
Go to www.outlook.com, login. Click your username at the top right, click "Account Settings". Click Overview > Add or Change aliases > Add alias (or remove). Make an account email
b) To set the new alias as your primary one:
Go to http://account.live.com. Click account aliases. Click "Make Primary" under your new alias.
c) To remove the original email address, go to step a).
NOTE: THIS WILL REMOVE ALL YOUR EMAILS IN YOUR OLD EMAIL AND NOBODY WILL BE ABLE TO CONTACT YOU UNTIL THEY KNOW YOUR NEW EMAIL ADDRESS!!