WoodMart theme allows creating custom labels and attaching them to products in the store. In general, custom labels are simple product attributes as well as size, color, or any other. They are created in Dashboard -> Products -> Attributes -> Label (title of an attribute) -> Configure terms.
You can create one or more items, assign them to the simple product and enable "Show attribute label on products".
If there is no image uploaded to the attribute item, the text would appear on the product grid and on the main product image. Labels with an image would have been presented as the image.
The label shape is configured in the Theme Settings - > Shop -> Labels.