Drupal Commerce: how to add "Middle name" field to the "Address" pane?
You can add the field under store -> customer profiles -> profile types -> Billing Information -> Manage Fields (Or go to admin/commerce/customer-profiles/types/billing/fields)

You can add any additional fields there. You can't add any fields directly to customer_commerce_address, but if you add any fields under the Billing Information they will show up during checkout.