Ukraine means "[on the] frontier" or "borderlands". Ukraina is pronounced the same as Krajina (minus the "oo" part at the beginning), the frontier between the old Austro-Hungarian and Ottoman Empires in the Balkans. The reason ignorant people call it "the Ukraine" (and think they sound smart doing so -- eye roll) is because the region was once called that for obvious reasons "the frontier" or "the borderlands". It's kind of like how some people ignorantly say "the Sudan" meaning the country, when "the Sudan" actually refers to a region that does not conform in any way to the present country.
Anyway, Ukraine was never its very own country until 1991. And the borders in the area of Ukraine have certainly shifted over time:
If you want to go all the way back to the Sarmatians ... the Slavic tribes (not Ukrainians or Russians yet!) that coalesced around the Viking rulers of Kiev likely mixed with them and whoever else was toodling around the area, too, before the Mongols rode in and whooped up on everybody and split the Rus in two (and the languages began to diverge, with Belarusian and Ukrainian being more alike than Ukrainian and Russian). Yes, there was more Russian assimilation of Finno-Ugric peoples.
There are still tiny pockets of Hungarians, Romanians, etc., on the western and southwestern edges of Ukraine.
As you can see on this old map of the Austro-Hungarian Empire, Lemberg (Lvov, Lviv) was considered a Polish city, even though it was in the eastern or "Ukrainian" part of Galicia:
Ukrainians and Russians intermarried, crossed back and forth between Russia and Ukraine the same way we would cross a state line, as from Texas to Oklahoma, during Soviet times, and most considered themselves more alike than different. Well into the 1990s, Ukrainians still consumed lots of Russian language media, etc. Of course many became more Ukrainian in identity and exaggerated differences, especially after the 2014 coup and even more since the Russian invasion, even some who speak Russian at home.
Back to eastern Galicia/western Ukraine, the Poles were still very much around into the 20th century. Between first the commies, then second, the nationalist Ukrainians who ethnically cleansed them during the 1930s, and third, after WWII, Stalin, not so many left there now. See: https://en.m.wikipedia.org/wiki/Poles_in_Ukraine