Here are the steps to be followed if you want to use your Outlook alias as the default email account for sending replies.
Step 1: Login to Hotmail or Outlook account and click the settings icon available at the top right hand side corner.
Step 2: Select More mail settings option from the settings menu list.
Step 3: In the Mail Settings screen, navigate to Managing your account and click the Sending/receiving email from other accounts.
Step 4: In the Sending/receiving email from other accounts screen, navigate to You can send mail from these accounts section and click the Add another account to send mail from option.
Step 5: Now enter your Hotmail or Outlook alias email address in Add an email address field and click Send verification email button.
Step 6: After the accepting the verification email, the alias email account should appear under the You can send mail from account accounts. Now click the Use as default option to make the alias email address as the default account for sending all replies from your Hotmail or Outlook account.