You are confusing many things.
The Rus were a people, not confined to the modern nation state of Russia. Modern Russians and modern Ukrainians can both equally claim Rus ancestory. Neither more than the other.
Yes, Ukraine was the center of Rus civilization for several centuries. That it was not the geographical center doesn’t matter. Very few civilizations have had a geographical center.
Indeed, the name Ukraine, as it is now applied, likely came into common usage during the period of Polish control, and its reference to the area as “a border” was in reference to the border of their control. Not as you imply, that somehow it was always considered a border possession of the Russian people.
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.