Thank you very much for your suggestion, and thank you Lee for the caution. We do have the Product Features extension purchased in September (it didn't work as expected back then, as products could not be found in Search by created features, so it was disabled for good). This extension can help show more in the product details yes, however we already have the standard product description just enough to explain our products, and the tags to alleviate search, so the keywords and product details are not a problem (and the extension is switched off). The problem is on the page of the products listing where extension is no help (we have tested), the listing of products returned by the Search:
public_html/storefront/controller/pages/product/search.php
public_html/storefront/view/default_html5/template/pages/product/search.tpl
public_html/storefront/view/default_html5/template/pages/product/product_listing.tpl
The list from the search only shows you a product name, image and price. There is no way to show other details or hints, no mention of parent sub-categories of listed products, or any other descriptions. This is OK when every product's unique, or consumers do not care which category their products have come from.
But when you have 3 level categories (model > brand > year), and most products have somewhat similar names that can be distinguished only by opening product description, this is when you will get confused by 10 weirdly looking Solenoids found in Search. If only consumers saw their Level 2 category (Brand) under each product's name ( not even Level 1(Make) or Level 3(Year), which are no big help for the identification!), that would do it but there's no setting for it.
As we understood, this is a hard coded behavior that cannot be changed (likely initially designed for very simple and small web-stores). All we can do is to type the names of Level 2 categories into the Product Name field after the product names for each product we have, or even stamp it onto the product photos... We know this isn't good looking solution but that's the only one we are seeing... Hopefully it helps others who have to deal with more complex inventories.
Just a thought, a better solution could be having one more variable in product parameters (say "Product Alias"), that could contain additional name or a brief description, that could be presented in the product Listing found by Search -- just below each Product Name in a smaller-sized font. That would make it for our consumers. Sorry, we should have created this topic in the new features suggestion but didn't realize it back then.