Pass an extra hidden value of a product

hi,

I would like to add extra information of my product, based on the search term that my visitor does.
So if a visitor search for “ball”, my product will be called “product ball”. Possibly I would like to store the term “ball” also as an information (maybe an attribute?) that is related to the order of that product.

The visitor can search for any term.

any idea how I can do that?