It'd be easiest to just have several search boxes, each pointed at one language's worth of fields. Conditional display the correct one for the selected language.
Field names are what they are. They're not labels and they cannot be changed on-the-fly. Just like in the Current Selections Object. But while you can recreate your own Current Selections object that does support name changes (or labels), it will be pretty difficult to do that in a Search object...
