Add Hidden Field to Forms

I would like a new form field that lets us create a form field that is hidden from the customer.

So when they place an order and fill out the form on the product page or on checkout, we can have additional information along side the form that we can see in the backend, but isn't visible to the customer.

For example, a form to customize a product may ask the customer for their name to customize an item. There could also be a hidden field with other text, so the customer only sees the name field, but when we view the job summary pages from the backend, we also see some other related text, like instructions for a vendor on how to split a name between one and two lines. Or information for a 3rd party system, etc.