That is, the censor is some bored middle-class beaurocrat rather than a true believer. So all you need is to give the him plausible deniability so he can turn around to his bosses and say "Hey, he redacted the name, how was I to know he was talking about your mother."
It was not the case at the time. Censors were bright guys, including e.g. great writer Goncharov, or Nikitenko, who hadn't written any novels, but left very thoughtful memoires. On many occasions censors of controversial books were reporting to the tzar personally, or were tzars themselves (e.g. Nikolay I censored Pushkin).
Most 19th century was depressing and stagnant time wrt politics, so books drew immense public interest.
That said, op's example would be automatically censored by the author himself, since this language was unprintable in 1860s.
I don't know about the Dostoevsky's places, always thought it was a traditional trope - places named with the first letter are ubiquitous in Russian novels.
Edit: also, it's worth noting that much censorship was made to make books suitable for morally unstable or easily agitated demographics, like women, so sometimes the motives for a particular edit could be hard to relate from modern relativistic perspective.
Oh, I'm aware of place names and certain people beginning with just the first letter (such as 'Prince S.' in 'The Idiot'), but certain words were blanked out with stars, such as 'B*'. It happened only a handful of times in 'The Idiot', sometimes for a name a occasionally for a place. I don't recall that form of redaction ever appearing in 'The Karamazov Brothers', though.
That is, the censor is some bored middle-class beaurocrat rather than a true believer. So all you need is to give the him plausible deniability so he can turn around to his bosses and say "Hey, he redacted the name, how was I to know he was talking about your mother."