I recently started reading Anna Karinina, and it is a bit annoying to me that they always refer to someone with their first and middle name! I understand in introductions you would use the first, middle, and last name, as I believe all 3 were very identifying at that time. However, in casual conversations, they continue to use first and middle names - two brothers, discussing their 3rd brother, always refer to him with both names. Is there a reason for this? I don't think I have noticed this with other literature of the time, though I have probably only read American novels, was this a Russian thing?
Russians didn't (and don't) have middle names, like Americans do. Russian naming conventions provide for a personal name (imja), a patronymic (otčestvo), and a family name (familija). A patronymic is usually shared by all of a given man's children, while a family name is passed down through generations as family names typically are.
Russian does not generally use titles like Mr., Ms., etc. for formal address, and instead achieves the same effect with the personal name and patronymic (as an aside, if you're reading a translation of Anna Karenina that preserves this convention, it's likely that there's a mention of this in the translator's notes at the beginning of the book). As in English, formal forms of address can signal positive things like respect, but also neutral/negative things like distance. Typically, family members, even in noble households with exceptionally strained relations (like the Bolkonskys in War and Peace), address each other informally. Even though Koznyshev is estranged from Levin, it would be unusual if they addressed or referred to each other formally, and it seems more likely to me that the narrator is referring to him as Sergei Ivanovich to emphasize to the reader that the character is not to be sympathized with. A citation to a particular chapter where this happens would be useful, though.