Add First Name & Last Name field on the WordPress registration form.

custom-registration-fields.php

<?php
add_action( 'register_form', 'loginpress_plugin_register_form_custom_field' );
function loginpress_plugin_register_form_custom_field() {

  $first_name = ( ! empty( $_POST['first_name'] ) ) ? trim( $_POST['first_name'] ) : '';
  $last_name  = ( ! empty( $_POST['last_name'] ) ) ? trim( $_POST['last_name'] )   : ''; ?>

  <p>
    <label for="first_name">
      <?php _e( 'First Name', 'loginpress' ) ?><br />
      <input type="text" name="first_name" id="first_name" class="input regular_text" value="<?php echo esc_attr( wp_unslash( $first_name ) ); ?>" size="30" />
    </label>
  </p>
  <p>
    <label for="last_name">
      <?php _e( 'Last Name', 'loginpress' ) ?><br />
      <input type="text" name="last_name" id="last_name" class="input regular_text" value="<?php echo esc_attr( wp_unslash( $last_name ) ); ?>" size="30" />
    </label>
  </p>
  <?php
}

// 2. Field validation.
add_filter( 'registration_errors', 'loginpress_plugin_registration_errors_custom_field', 10, 3 );
function loginpress_plugin_registration_errors_custom_field( $errors, $sanitized_user_login, $user_email ) {

  if ( empty( $_POST['first_name'] ) || ! empty( $_POST['first_name'] ) && trim( $_POST['first_name'] ) == '' ) {
    $errors->add( 'first_name_error', __( '<strong>ERROR</strong>: You must include a first name.', 'loginpress' ) );
  }
  if ( empty( $_POST['last_name'] ) || ! empty( $_POST['last_name'] ) && trim( $_POST['last_name'] ) == '' ) {
    $errors->add( 'last_name_error', __( '<strong>ERROR</strong>: You must include a last name.', 'loginpress' ) );
  }
  return $errors;
}

// 3. Lastly, save our extra registration user meta.
add_action( 'user_register', 'loginpress_plugin_user_register_custom_field' );
function loginpress_plugin_user_register_custom_field( $user_id ) {
  if ( ! empty( $_POST['first_name'] ) ) {
    update_user_meta( $user_id, 'first_name', trim( $_POST['first_name'] ) );
  }
  if ( ! empty( $_POST['last_name'] ) ) {
    update_user_meta( $user_id, 'last_name', trim( $_POST['last_name'] ) );
  }
}
?>