Commerce module uses Rules module extensively. Unlike Ubercart where you can just call a hook and receive $account information of the final process once an anonymous user is converted to a Drupal authenticated user, once checkout is complete.  With Commerce we have to use Rules to create a custom rule with an action that ultimately executes a callback....Yes, I know....

Here's the example of what we did. Look at the code comments for a better hint of what is going on.

/**
 * Implements hook_default_rules_configuration().
 */
function yourmodule_default_rules_configuration() {
  $rules = array();
  $rule = rules_reaction_rule();
  $rule->label = t('After new user is created');
  $rule->active = variable_get('mymodule_append_data_to_new_user', TRUE);

  $rule
      // We use a system event.
      ->event('user_insert')
      // action() is smart enough to know this is a
      // custom action that we'll define later.
      ->action('add_data_to_user_object', array(
        'type' => 'user',
  ));

  // Execute after similar rules.
  $rule->weight = 10;

  // The unique machine name of your rule.
  $rules['yourmodule_append_qbo_customer_id_to_new_user'] = $rule;

  return $rules;
}

/**
 * Implements hook_rules_action_info().
 */
function yourmodule_rules_action_info() {
  $defaults = array(
    // Defines parameters that are passed to
    // your callback.
    'parameter' => array(
      'account' => array(
        'type' => 'user',
        'label' => t('User'),
        // Tells Rules to save any changes made to $account.
        'save' => TRUE,
      ),
    ),
    'group' => t('User'),
    // Rules built-in access.
    'access callback' => 'rules_user_integration_access',
  );
  
  // The name of our custom action that was defined in
  // ji_commerce.rules_defaults.inc.
  $actions['add_data_to_user_object'] = $defaults + array(
    'label' => t('Insert a new user'),
    // Finally, our callback!
    'base' => 'yourmodule_action_insert_new_user',
  );
  return $actions;
}

/**
 * Callback: We run QBO calls here. Since with Commerce
 * we can't do it within the hook_commerce_checkout_complete().
 */
function yourmodule_action_insert_new_user($account) {
  // This change will automatically be saved by Rules.
  $account->data['some_id'] = 100;
}