Just adding something to this. Right now, both the city (703448 ) and the ADM1 (690791) are named in geonames as 'Kyiv'. However, the countryInfoJSON API is still returning 'Kiev' for the capital, so there seems seems to be at least an inconsistency in that.
As for which one is right, according to wikipedia, since 1991 the official way seems to be Kyiv. If we follow the logic of Czechia (where the countries choice trumps the commonly used), then I suppose Kyiv should be the one.