The word "Ukraine" as a nation name, I believe dates from the 1990s. However, material culture in the region has been found dating to as far back as 5000 years ago. Material culture is archeological artifacts with a commonality of identity. And, "western" versus "eastern" is as valid as "northern" versus "southern" in any geographical sense. Again, much more of the country on such compass determinates would have been Scythian Iranian which dominated a southern region perhaps three times the geographical area of the northern region which encompassed the Kievan Rus culture; note, that "Kiev Rus" state also claimed much of what is now Poland. The Kievan Rus are only extended a little south of what is modern day Kyiv. The Scythian Iranians extended as far north as the Pontic Steppes to the Black Sea, into what is now Ukraine, including encompassing ALL of the Caspan Sea.
If we allow Putin's claim – which is demonstrably a lie – that Ukraine has "always been Russian," then what more lands might he claim under the same premise?
Whatever they choose to call themselves today, they are a singular people allowed to claim their own unique identity. While they may have been forced to be Russian a few times in their history, they have always been their own people.
By Putin's own logic, and by the historical and archeological record, Kyiv might claim to be the heart of the true Rus and justify some future aggression attempting to take back the territories of the old Kievan Rus state. They too would be lying. The past belongs in the past. People have the right to choose who they will be and with whom they may ally themselves.
Putin has made Russia like a possessive, violently abusive boyfriend. He will always claim what he convinces himself used to be his. Putin has Russia killing Ukraine because he believes it belongs to Russia. And, if Russia can't have it, then it must die.