Hello,
You may try third-party plugin to add labels for products that have this option. For example https://wordpress.org/plugins/aco-product-labels-for-woocommerce/ https://wordpress.org/plugins/advanced-product-labels-for-woocommerce/ or similar that will suit your needs most of all. Or submit an additional customization request here if you want to order additional customization to create such feature on your site.
Regards
