If your Hotmail address doubles as your primary Microsoft account and you use it to sign in to your devices, renaming your email with an Outlook.com domain will require you to reconfigure your devices to log in to the new account rather than the old Hotmail.com address. Windows Phone users will need to perform a factory reset on their handsets to do that, which will wipe all the apps and personal data from the phone. You can freely reinstall the wiped apps, but the personal data will be gone forever if you don't back it up first.
A better alternative is to just change your e-mail address using an alias. Outlook, like Hotmail before it, allows you to set-up alternative e-mail addresses called aliases that can deliver e-mail to the same inbox as your primary account. The beauty of this approach is that you can use your alias as your default address and still receive e-mail sent to your old address. And, if you ever get tired of your new Outlook.com alias, you can just trade it in for a new one without much hassle. The downside is that your aliases can't be used from a smartphone app or a mail client like Windows Mail. In these situations, you will only be able to send mail from your primary Hotmail address. You can create five new aliases per year up to a maximum of 15 aliases.
To get started, login to Outlook.com and click on the settings cog on the upper right side of your inbox screen. Then, in the dropdown window, select "More mail settings." On the next screen, select "Create an Outlook alias" under the "Managing your account" heading.
Now, just make sure "Outlook.com" selected in the drop down menu and then enter the alias you want to use such as firstname.lastname@example.org. When you're done, click "Create an alias."
If the address you're looking for is available, you will be taken back to your inbox and Outlook will ask you if you want mail sent to this address to go to a separate folder or to just throw it in the inbox. Since you plan on using your new e-mail address permanently, select "An existing folder:Inbox," and press "Done."
Now you've got your new e-mail address, but you need to tell Outlook to automatically send new mail from this address by default. Go back to you settings cog and select "More mail settings" again. Go back to the "Managing your account" heading and select "Your email accounts." On the next page, scroll all the way to the bottom and under the "Default 'From' address" heading, select your new alias from the drop down menu.
That's it, you're done. Now, all e-mails you send from Outlook.com will come automatically from your new address.