You might be correct that the term Ukraine is older than the term Russia in the Russian language. You are right as well that whatever meaning the term Ukraina may have, it does not come from Russian. It comes from Polish.

By the end of the 14th century, most of today’s Ukraine was under Lithuanian control. After the dynastic union of Poland with Lituania in 1386, for the next two centuries, Polish kings were giving Polish nobles so-called latifundia, basically vast pieces of land in what today is Ukraine. In old Polish, it was “u kraja” of the country, which means “by the edge.”

As you might know, those Polish settlements did not work too well for either side, but that is another story.