Create a custom WooCommerce product field. It is added in the inventory tab and displayed below the single product title.

wc-custom-product-fields.php

<?php

/**
 * Plugin Name:       Custom Product Fields for WooCommerce
 * Description:       This small plugin will generate and display a custom product field.
 * Version:           1.0.0
 * Author:            nvourva
 */

add_action( 'woocommerce_product_options_stock_fields', 'my_restock_notice_field' );
function my_restock_notice_field() {
  global $woocommerce, $post;
  woocommerce_wp_textarea_input(
    array(
      'id'          => 'my_restock_notice',
      'placeholder' => 'Back in stock next week!',
      'label'       => 'Restock notice',
      'description' => 'Let your customers know when the product will be back in stock.',
      'desc_tip'    => 'true',
    )
  );
}

add_action( 'woocommerce_process_product_meta', 'my_restock_notice_save_data' );
function my_restock_notice_save_data( $post_id ) {
  if ( 'no' === get_option( 'woocommerce_manage_stock' ) ) {
    return;
  }

  $my_restock_notice_textarea = $_POST['my_restock_notice'];
  if ( ! empty( $my_restock_notice_textarea ) ) {
    update_post_meta( $post_id, 'my_restock_notice', esc_html( $my_restock_notice_textarea ) );
  }
}

add_filter( 'woocommerce_single_product_summary', 'my_restock_notice_display', 6 );
function my_restock_notice_display() {
  global $product;
  $notice = get_post_meta( $product->get_ID(), 'my_restock_notice', true );
  $stock_status = $product->get_stock_status();

  if ( empty( $notice ) || 0 < $product->get_stock_quantity() || 'outofstock' !== $stock_status ) {
    return;
  } else {
    echo '<p class="my-restock-notice">' . esc_html( $notice ) . '</p>';
  }
}