If the name Ukraine came into usage during Polish control, today's name for that country would be Pograniczie. (Pograniczie - borderland in Polish)
Polish control of Ukraine was the control of Russian borderland, not vice versa.
Toponyms are tough cookie - they can not be stolen and destroyed to fit anyone's agenda. Even altered they are telling the story right. Toponyms are the original memes.
I don't concur, and neither do others. Don't know where you are getting your information, but ultimately it doesn't matter.
It could be called the land of the unfrozen southern Rus, and it wouldn't matter in regard to their current claims on sovereignty a bit. No more than the name Belarus does.
As co-ancestors of the Rus, Urkainians have as much claim over the areas controlled by Moscow, as Russians have over areas controlled by Kiev.