Sorry being dumb - can't remember how to edit posts
ANyway what I said above was essentially correct with the exception of:
"for males -ovich or evich, for females -ovna or evna,
and other points to note:"
"...patronomics can be used on their own but only humorously or condescendingly. "
Most given names have affectionate or dimuntive forms, as in English. It is hard to make general rules for them and, in the context of this book, not necessary. Most end in -ya (Boris - Borya) or -ka, -enka, -usha, -ushka, -usya. Thus Aleksandr:Sasha:Sashka:Sashenka;Pavel (Chichikov's first name)...
The first name (either its full form or its afectionately diminutive form) can be used with the surname, omiting the patronymic...."
This is taken and adapted from Nikolay Gogol - Dead Souls, a poem - Translated with and introduction and Notes by Robert A. Maguire, Penguin Classics 2004.
A good guide to Russian names. They are tough for Anglophone readers to understand - without taking a couple years of college Russian, that is.
I'll contribute a couple additions:
Patronymics can be used in combination with the first name (Ivan Ivanovich) as a sort of "affectionate formal". Name + patronymic, for example, is what you call your teachers in school as a kid. It's less formal than our "Mr. or Ms." in English so it can be used in some more casual situations where people are closer to what we would call "a first name basis" but not quite to the level of intimacy where Russians would use first names.
Also, when it comes to Russian nicknames, nearly every traditional Russian name has a standard set of nicknames (the various endings that Phlebas posted above show deeper levels of intimacy. Think of it as the difference between what your school chums, your girlfriend and your mom call you). These nicknames are much more prevalent than English nicknames, even when standardized. Typically, in modern English, people "pick a name" to go by. Some Williams go by "William" some by "Bill" others by "Will" depending on their personal preference and the tenacity of their close friends and family. With Russian names, nicknames just come with the territory. You don't run into a Russian (or, at least, I haven't) who says, "I prefer Rodion" when you try to call him "Rodya", unless you've overstepped your bounds in assuming intimacy. In other words, each Russian name implies a set of nicknames, depending on the intimacy of the person you're with.
For this reason, Russian authors use nicknames all over the place rather than picking one version of the name, like Anglophone authors do, to call a particular character. In Anglophone novels, you could have two characters, a "Billy" and a "William" without confusion as long as those names were used consistently and strictly for each character. It would be much harder in a Russian novel to have an "Ivan" and a "Vanya" without creating confusion.