This is an instance where a number of different terms are getting collapsed into a single English word "Russian", which is kind of confusing.

I say this because it's not really accurate to call the original Eastern Slavic group "Russian", and historians generally don't. The term very specifically used is "Rus'", which is a translitetation of Русь. The etymology isn't totally clear but it seems to be from an Old Norse term for rowers, or a region of Scandinavia associated with rowers (Rodslagen), and came to be associated with the state founded by the Varangians under Rurik (which is called "Kievan Rus'" because of its capital).

This version of Rus' was often Latinized as "Ruthenia" and Ruthenian was used to refer to these East Slavic lands, especially the ones that came to be controlled by Poland and Lithuania. Belarus (White Ruthenia) has kept that name but Black Ruthenia and Red Ruthenia also existed and referred to parts of western Ukraine/eastern Poland.

The state that developed in Moscow from the 15th century on used a version of this name for itself and its people: "russky" (русский), which also refers to the language that developed out of that area's dialect (although being a native speaker of that language was never synonymous with holding an ethnic identity of the same name). In 1721 that state adopted a new version of that name based on Greek: Russia (Россия), and anything associated with that state is rossisskii (российский). To make things more confusing, someone could be that kind of Russian without being an ethnic Russian or even speaking the Russian language.

Belarus kept a version of the "Ruthenian" name as Белоруссия, but what is now Ukraine was known from the 18th century as "Little Russia"/Malorossiya (малороссия), very much in the "Russian state" sense of the term. As a Ukrainian national identity developed in the 19th and 20th century it preferred just that name - Ukraine - over the Little Russia term, and the latter rapidly fell out of usage with the end of the Russian Empire.