Woocommerce custom attributes search

Hello,

bellow you can find 2 screenshots. As you can see on the product description of the my woocommerce product I have 2 tabs (1.Περιγραφή 2.Πληροφορίες).
The second tab has custom made attributes, one of them beeing Συγγραφέας, and when ever I search for the name of the attributes nod results are presented. But whenever the value of the attribute exist on the 1 tab the search brings back results.

Hello,

You can see bellow a screenshot of the admin area of wordpress. This my panel from woocommerce, for every product. As you can see there is the description, which is searchable,and ther there is a tab for creating attributes.

Yes I have enabled the search form to search product categories, but what Im looking for is neither a product category, nor a tag.

Hello,

No it does not and Ive tried your suggestion and it kinda works. Let me explain. Every product has a unique product number that users tend to search for. Adding the product numbers in a different page, other than the product as you understand is not the most efficient. So as this product number will be assigned to only one product at a time and not a category.

Is there a way to do the search without creating different product attributes for all of my products, and only using the custom ones that can be created directly from the product?