Yes, see examples in Polish in my reply to you?
Even its Wikipedia article uses Gdynia Główna as its name/title.
My guess is that the answer is yes. (Disclaimer: I lived in London for 2 years about a decade ago but I’m not really a Londoner.) If only because there is no other obvious destination named London Bridge. There is the bridge, of course, but it is not a destination of its own and so it’s unlikely the tourist wants to get out of the taxi right at the bridge.
I would bet that it’s also the case for all other central London railway stations like Liverpool Street or Waterloo, because the railway stations are major destinations.
Certainly if you get into a taxi in Gdynia and ask for “Gdynia Główna” you’ll be brought to the railway station. Non-tourists would probably ask for “dworzec główny” or “dworzec PKP”, but “Gdynia Główna” would be understood.
We have official_name=* if you want to do that – if you can find the definitive official name. (Particularly hard in England, where a lot of things are based on unwritten traditions.)
If you want to discuss naming standards for South Korea, it might be more productive to discuss this with other South Korean mappers and develop a local consensus, rather than asking about England and France and “some languages”.
Regions and communities are definitely allowed to have local guidelines that deviate from “worldwide” OSM guidelines (inasmuch as that even exists), and there is absolutely no requirement to have Korea OSM mapping guidelines match OSM guidelines for England or any other regions. If South Korean community wants to have “station” in their names, you can.