Lady Rasputina is not based on Grigori Rasputin, however, that is part of the joke. You see the game is somewhat of a post-apocalyptic-diesel-pulp that takes place on Mars. Lady Rasputina is a member of a Stalin-esque society's (Victoria Town) secret police (the Grigori) and is also an aristocrat.
Personality wise she is grating, boastful, sadistic, self-righteous, and chatty. In short, she's type of evil b---- that would have no qualms about feeding strychnine to an entire homeless shelter because 'it would solve the homeless problem.' Then after the last victim died she would give herself a congratulatory pat on the back then storm out of the building like Bender from the Breakfast Club.