Setting a FROM address in your Outlook.com email account will allow you to send email from an email at your domain name, for example: firstname.lastname@example.org
You'll need to set this up in your Outlook.com by following the steps below:
1. Log in to your Outlook.com account
2. Click on the cog in the top right hand corner
3. Select "Connected Accounts" from the drop down list
4. Click on "Manage or Choose a Primary alias" beneath "Email aliases"
5. On the "Manage how your sign into Microsoft" screen click on "Add email address" in the "Account Aliases" section
6. Add the email address you'd like to use and press "Add Alias".
7. Outlook will send an email to the new email address. The email will contain a validation link which you will need to click on to verify that you are the email address owner.
8. Once verified return to the "Connected Accounts" area and click on "Change your From Address""
9. Select Your new email address from the drop down and click the "Save" button above.
You new email address will now be the default email address used when you send emails from your Outlook.com account.