Razumikhin
I’m up to volume 4 in Joseph Frank’s 5-volume biography of Dostoevskii and his reading of Crime and Punishment. Without dwelling on it (so far at least), he mentions that the name Raskolnikov “evokes the Russian word for a schismatic religious dissenter, a raskolnik” and the name Razumikhin “contains the Russian word for ‘reason,’ razum” (98–99). Frank says that naming Razumikhin after reason is evidence of “Dostoevsky’s desire to link the employment of this faculty not only with the cold calculations of Utilitarianism but also with spontaneous human warmth and generosity” (99). There’s also an interesting footnote on Dostoevskii accidentally writing Rakhmetov in his notes when he means Razumikhin, and Razumikhin saying that his name is an abbreviation of the original form Vrazumikhin.
It’s a small thing, but I’ve always wondered why everyone explaining “Razumikhin” for an Anglophone audience works from razum. It’s just the -in ending that’s one of the standard endings for Russian surnames (along with -ov/-ev). The -ikh- is something else. To my non-native ear it sounds like the obsolete form razumikh, as in азъ разумихъ. (Is the proper aorist form азъ разумѣхъ? You can find examples of both.) After all, the name could have been Razumov or even Razumin; both exist, and the first is reasonably common. Razumov/Razumin would still have meant reason, and the warm kind of reason instead of the cold rassudok. But Razumikhin has, if I’m not mistaken, the additional suggestion of ecclesiastical language, the Church, and Christianity.
XIX век 
It’s because of the “form of Vrazumikhin” passage. “Vrazumit'” means “to make one see reason” or “to teach one” as in “I’ll teach you to steal my apples!” or “Her father’s words made her see reason and change her ways”. There’s no suggestion (imho) of either cold or warm reason, but some ecclesiastical overtones may be seen in the connection to a clergyman’s duty to bring his stray sheep to reason (“vrazumljat’ pastvu”).
What do you make of the -их- suffix? Could the last name Вразумихин bring to mind вразумихъ, from вразумити, and have ecclesiastical overtones via the Old Church Slavic verb form (in addition to the possibility of вразумлять паству)? I’m on shaky ground here, both with церковнославянский язык in general and with how such forms sound to native speakers of modern Russian. Thanks for the insight into вразумить and what it implies!
I’m not a native speaker of modern Russian 😦 My Russian is dated by a generation or so. That said, to my ear there are no Slavonic overtones there at all. It’s just that “Vrazumin” and “Vrazumcev” are not possible, unlike “Razumin” and “Razumcev”. No idea why, but these sound as wrong to me, as pronouncing the “k” in “knight” would to a native English speaker.
Also, I think the Church Slavonic explanation is too complicated. There is a simpler one available, based on a difference of meanings. Razumin is one who has reason. Razumcev is the same, but in a lower or a more comical sense. Razumixin, however, is more apparently one who “razumeet”, that is one who understands or knows or even one who has understood. This word is not actively used now, but is understandable to all Russian speakers. It is still used in the meaning “to know” or “to understand” in Ukrainian and Byelorussian. In Dostoyevski’s time one could say “ja ne razumeju francuzkogo” i. e. “I don’t understand French”. Another example would be Musorgski’s statement “I razumeju the people as a great personality”
Actually, never mind, I do know why Razumin is possible, and Vrazumin is not. Because the first is based on a noun, and the second on a verb, and you can’t have a quality of a verb. D’uh.
Thanks again for your comments. By “modern Russian” I just meant as opposed to Old Russian and Old Church Slavic, and really the ideal informant would speak Russian as it was spoken six or seven generations ago! It’s quite interesting that, if I understand correctly, Разумихин sounds like it comes from разуметь rather than the thoroughly obsolete verb разумѣти or the noun разум.
Well, not necessarily “comes from”, but “associates with”. I think most people will form associations with the newer and more familiar to them verb, although it, of course, comes from the obsolete one and has the same root as the noun.