I can't give you an exact date, but what I can do fairly confidently is give you a range in which the shared identity developed.

Terminus Post Quem: Olga's raid against the Drevlans (c. 950). Drevlans were an Eastern Slavic tribe, specifically named as a group that Igor, Olga's husband and Grand Duke of Rus was collecting tribute for (in their tribal centre, named Iskorosten). This means that there were definitely separate identities at the time between numerous Eastern Slavic tribes inhabiting the lands of Kievan Rus. No "Ruthenian" identity between the populations existed at the time.

Terminus Ante Quem: "The Tale of Igor's Campaign" (Слово о плъку Игоревѣ) - an Eastern Slavic epic about Igor's (different Igor, living over a century later) campaign against a Turkic Cuman tribes. The epic contains numerous references to Russian identity in opposition to non-Russian Cumans (Polovtsy) and certain other groups (identified with, for example, Avars). The epic is considered to have been written in the late 12th century.

This gives us a range of around 950-1200. Considering that the ideas in the "Tale" seem to have been mature and were unlikely to be an invention of the author, the identity developed earlier than that. Obviously, it took some time to develop "Ruthenianism" after 950, too. So we know that at least some people (the elites) started thinking of themselves as Russians some time between the years 1000 and 1150.

PS. A bit on terminology, before I get eaten alive by my compatriots, among others (I'm Belorussian myself): I use the term "Russians" for all of the Eastern Slavs. This community broke apart after the Mongol invasions into eastern and western branches (Russians and Belorussians/Ukrainians), after which the western branch further broke apart into northern and southern groups by the Lublin Union which gave Ukraine to Poland. Nowadays there are three separate nations with three separate languages descending from these original "Russians". But in the middle ages - they were all Ruthenians (Руськие).

IIRC, most early russians were a variety of nomadic people living in the steppe above india, before they finally started spreading around the area now known as russia, and in the (12-1300's?) founded kievan Rus, the progenitor to Kiev.

True russian nationalism started at the end of the Time of Troubles around 1600, after Russia had been invaded multiple times by Poland and Lithuania, and had several false successors to the Romanov throne attempt to claim the inheritance. Finally the russian citizens decided they'd had enough, and two farmers (Kuzma Minin and Dmitri Pozharsky) led a small army of citizens to expel the Polish and take back the country.

This is a holiday still celebrated in the present day in Russia, and I would consider it the start of true nationalism, even though there was monarchical rule before and after the event.

edit: it seems the holiday was abolished by the bolsheviks in favor of celebrating the october revolution, and reinstated by putin in 2005, but almost no russians now understand the significance of it.