Keep in mind that if an alias is deleted any email sent to that email address will be returned to the sender as undeliverable (unless you have a catch-all mailbox). If you want to continue receiving email sent to the old alias, you could reassign it or leave it in place and create an additional alias.
To delete an alias:
Visit your Email Control Panel.
Click the "Edit User" link under the name of the person currently managing the alias.
Email Control Panel - Edit User Link
On the Edit User page, click the "Delete" link next to the alias.
Email Control Panel - Edit User: Delete Alias Link
On the following page, click OK if you're sure you want to delete the alias.
Email Control Panel - Edit User: Delete Alias OK Button
On the confirmation page, click the Finish button.
Email Control Panel - Edit User: Delete Alias Finish Button
You can recreate this alias at any time by returning to the Email Control Panel and clicking "Add Aliases."