I took a survey on Russia a few semesters ago, and one of the things that stuck out to me were numerous instances in history in which seemingly random people claimed to be long-lost heirs and led insurrections. There were the three False Dmitriys and Pugachev claimed to Peter III. I think there might be others that I am forgetting (without even considering the modern Anastasia myth).
Was this sort of a culturally perpetuating thing, or did it have some roots in Russian aristocracy/autocracy?
Hey so I know that this was five months ago, but maybe you're still interested?. I don't know too much about the false Dmitriys, but around the time of the Pugachev, Russian society very much loved the Tsars. They saw the Tsar as a father (or mother) figure, a religious leader, and a leader of the country. Almost anytime things were going badly for peasants, they blamed everyone besides the Tsar. When things were very bad in Russia, many of the peasants went as far as to claim that the current Tsar was an imposter. For example during Peter the Great's reign, many peasants were discontent with the war against Sweden and his controversial reforms. But the revolts of the time (Bulavin and Razin) didn't aim to overthrow the Tsar, they instead wished to "free him from the nobility", who they thought were bullying Peter into oppressing the them. Some even claimed that the Peter had been secretly replaced by a stand-in.
So what's the point in me telling you this? Well, in short, when the peasants of Russia wanted to believe that the Tsar couldn't possibly do anything to harm them, but the Tsar was doing something to harm them, many of serfs became convinced that the actual Tsar wasn't the real Tsar. And because of this, a few individuals took advantage of this to gain power and influence over their peers. Most of these people actually caused relatively little harm, and could hardly be considered revolutionaries.
As for Pugachev, he claimed he was Tsar Peter III, but the rebels mostly just used that as a cause to rally behind, and hardly any of them actually believed he was really the Tsar. At that point the peasants were basically just looking for an excuse to rebel, because that time in Catherine II's reign marked the absolute low point of peasant living quality in Russia.
tl;dr: Russian peasants really wanted to like the Tsar for religious and other reasons, so when the Tsar did something wrong, they sometime believed that he/she had been replaced by an imposter. Because of this, it was easy for people to claim to be the "actual" Tsar and gain power/money/influence.
Sources:
Paul Avrich, "Russian Rebels 1600-1800"
Geoffrey Hosking, Russia: People and Empire
My History professor