Hello,
I saw the screenshot you attached.
To create a custom badge you need to create an attribute from Products >> Attributes.
Screenshot for Clarification: https://ibb.co/2ZkML5z
Then you need to assign the attribute to the specific product from Edit Product.
Screenshot for Clarification: https://ibb.co/0ZDfBKL
Then from Products >> Attributes >> Edit Attribute.
Screenshot for Clarification: https://ibb.co/k9sYR83
Enable the option show attribute label.
Best Regards