It really is time the "International" stations were renamed. It was of questionable value when Eurostar did occasionally serve them, and is just plain misleading now. It would also be clearer to drop it for the "domestic" bits of St Pancras. Stratford International, which has never been served by any continental train, is of course at a level of ridiculousness all of its own!!
Indeed - leaving Birmingham International, Harwich International and Prestwick International Airport with the word in their names ...
However unlike the above mentioned St Pancras International, Stratford International, Ebbsfleet International and Ashford International have a legally defined international frontier / border post within the station the above do not.