Hello,
Woocommerce does not provide such an option, unfortunately. You can create an attribute and create a “Free” attribute item, add it to the product and enable “Show attribute label on products” in Products > Attributes > enter the attribute which you have created. You will get the label on the product and your price. The product would be added without any problems.
You will need to hide the existing label:
Please add this code to the Theme Settings > Custom CSS > Global:
body .labels-rectangular .onsale {
display:none;
}
Best Regards