How to customize a Wordpress Multisite (WPMU) registration form

functions.php

<?php
/**
 * Customize the MutltiSite Registration Form
 */
//1. Add a new form element...
add_action( 'signup_extra_fields', 'mydomain_register_form' );
function mydomain_register_form( $errors ) {
  // First name
  $first_name = ( ! empty( $_POST['first_name'] ) ) ? trim( $_POST['first_name'] ) : '';
  echo '<label for="first_name">' . __('First Name:') . '</label>';
  if ( $errmsg = $errors->get_error_message('first_name_error') ) {
    echo '<p class="error">'.$errmsg.'</p>';
  }
  echo '<input name="first_name" type="text" id="first_name" value="'. esc_attr($first_name) .'" maxlength="60" /><br />';
  _e( '(Must be at least 4 characters, letters and numbers only.)' );
}

//2. Add validation. In this case, we make sure first_name is required.
add_filter( 'wpmu_validate_user_signup', 'mydomain_registration_errors', 10, 3 );
function mydomain_registration_errors( $result ) {
  if ( empty( $_POST['first_name'] ) || ! empty( $_POST['first_name'] ) && trim( $_POST['first_name'] ) == '' ) {
      $result['errors']->add( 'first_name_error', __( '<strong>ERROR</strong>: You must include a first name.', 'mydomain' ) );
  }
  return $result;
}

//3. add meta for the pending user.
add_filter( 'add_signup_meta', 'mydomain_signup_meta' );
function mydomain_signup_meta( $meta ) {
  if ( ! empty( $_POST['first_name'] ) ) {
      $meta['first_name'] = $_POST['first_name'];
  }
  return $meta;
}

// 4. Finally, Set new usermeta upon new user activation
add_action( 'wpmu_activate_user', 'mydomain_activate_user', 10, 3 );
function mydomain_activate_user( $user_id, $email, $meta ) {
  if ( $meta['first_name'] ) {
      update_user_meta( $user_id, 'first_name', trim( $meta['first_name'] ) );
  }
}