I am trying to work out what case goes with kereső. I wondered about -ért as the notion of "for the purpose of". Can you say "kereső valamiért" to mean "searcher for a thing", a something finder?
Search Engine is simply "kereső" in coloquial Hungarian. Wasn't it that you meant?
For example, in tools and programs where there is the searching screen popping up or there is a searching line somewhere, we call it: "a keresője" or more precisely: keresőmező