When using https://nominatim.openstreetmap.org/search?q=geneva&countryCodes=CH&addressdetails=1&format=json&accept_language=en I still get “Genf” as a result and not “Geneva” if the browser language is de. How can I get the English name?
Using the correct output (and filtering) parameter does help:
accept-language instead of accept_language, see Search - Nominatim 4.3.2 Manual
You probably want to use countrycodes instead of countryCodes too.