Pull Form fields into Woocommerce product and checkout?

I have an online store selling virtual items - in this case, dance classes for children. Users enter their registration details on a Formidable form, including their child's name. However when they come to purchase a series of classes, I currently require them to re-enter their child's name in a custom field for that product, so that we know which child the purchase is for. It would be more user-friendly for the customer if I could pull that info directly from the Form. Sometimes the parent has more than one child but needs to buy different classes for each child, so it would be good if they were provided with a dropdown menu to select the relevant child.

Does anybody know if this is possible? Would this be easier / possible if I purchased the Woocommerce add-on for Formidable?