I recently read 'The Idiot', translated by Ignat Avsey (I enjoyed his 'Karamazov Brothers' translation), and it contained a few similar redactions with no notes as to why. I thought it was maybe just a stylistic device.
It is indeed a common literary device in 19th century Russian lit. Usually with proper names to make them more "anonymous" but contemporary readers would know exactly what was being referenced.
For example, most of the place names in Crime and Punishment are redacted, but it's so clear where everything happens there are walking tours in St Petersburg.
In my copy of Crime and Punishment it has some names (especially place names) where the end notes say it was partially redacted to get the manuscripts past censors. Not necessarily the case for every redaction 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."
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.
For example, most of the place names in Crime and Punishment are redacted, but it's so clear where everything happens there are walking tours in St Petersburg.