That's not entirely true. Kiev derives from the Russian Ки́ев, whereas Kyiv derives from the Ukrainian Київ--note that the Cyrillic orthography differs between the two languages.

One of the main reasons for the conscious effort to shift spelling is the fact that Russia is trying to invade Ukraine partly on the basis that Ukraine wasn't actually a real country and Ukrainians are just Russians. In that context, using Russian place names over Ukrainian place names for Ukrainian localities can be seen as a tacit endorsement of this claim, and this is why so many entities are consciously making efforts to use translation from Ukrainian, rather than Russia. (Although I, and apparently many others, seem to have to a hard time with "Odesa/Odessa").