Hello,
To allow customers to enter their engraving details when ordering, you can make your product customizable by adding a custom text field.
You need to find a third-party plugin to achieve more functionality that best suits you.
https://wordpress.org/plugins/advanced-product-fields-for-woocommerce/
For Example, create a Text Input Field and assign it to your engraved tags product. Customers can type their engraving text, and it will be included in their order details.
Best Regards,