Earlier quoted context omitted.
Indeed. “Rus” is an ethnonym, of famously Scandinavian origin, used across the entire East Slavic area and was never something limited to people in now-Ukraine that people in now-Russia could “steal”. The Uralic- and Turkic-speaking peoples of the Middle Volga, for example, already called the neighboring Slavic-speaking populations “Rus” in the medieval era.
Actually no. "Rus" was meant to describe "all" East Slavic people, but Russians took it for themselves "only" and started to call Ukrainians "Little Russians" in sense of "Lesser Russians".
And "Little Russia" is an old name of a geographical region (which somewhat corresponds to the traditionally Russian-speaking parts of Ukraine).