Old East Slavic speakers called their language "Rusian", which is, as everyone can see, most certainly not "Russian".

They didn't rule Kiev, though. Lithuanians (who spoke proto-belarussian, ergo "Кіеў") and later Poles did.
For those who don't know it: there is little difference between how i and e are pronounced in Kyiv or Kyev. The e would be prounounced close to an i, anyway. The second letter in cyrillic, the и, is the same in both the Russian and Ukrainian name of the city, it's just that Russians pronounce and transliterate it as an i, while Ukrainians pronounce and transliterate it as an y.
It's a potayto - potahto or harbor - habour kind of issue, really, which is currently sadly supercharged by war and nationalism. Before 19th century, east slavic languages didn't even have proper orthography, which makes arguments over those things even sillier. There is no way to know how people would have pronounced the name of the city in 1444. Kiyew, Kyyew, Kiyow, Kyyow, Kyiw, Kiiw, Kiou - probably different people pronounced it differently, as nobody made a big deal about it. Sometimes, same people pronounced it differently on different days, on different occasions, when speaking to different people. They didn't have rigid rules on how to pronounce sounds.
Yeah, you have Kyiv for diplomatic reasons, and still have "Kievan Rus" rather than "Kyivan Rus". Language is a messy business, and yes, attempts to insist on one name instead of another is just politics. Ottomans can have Konstantiniyye on the map while their trade node is called Constantinople. Poland is called Poland rather than Polska, and Lithuania is called Lithuania rather than Lietuva.