Create a form to capture personalization for products and include product ID

I’ve been tasked with setting up a WooCommerce website. My skills are mostly design based.
There are multiple products are personalized. I’m sure I can use a simple form to capture the personalization information. But can I add a hidden field that would self populate something that identifies the product page that the personalization was entered on, so that when I retrieve the form entry I can know which product gets which customization?

Hi Michael. Are you already using this plugin to integrate Gravity Forms and WooCommerce?