What about generic or almost generic trademarks? If I search for something like bandaid I am certainly _not_ expecting Google to rank Johnson and Johnson (the o

What about generic or almost generic trademarks? If I search for something like bandaid I am certainly _not_ expecting Google to rank Johnson and Johnson (the owner of the trademark for bandaid) above other potentially more relevant results. And the same applies to other terms like Kleenex, Ziploc, aspirin, etc.