Russian patronymics

Or the Russian naming system. The first portion of a Russian's name (and possibly in other Orthodox countries as well) is a saint's name, generally one of the saints that is celebrated on the child's brithday or eight days later - because eight days after the birthday is generally when children are baptized.

The second portion denotes who the child's father is, by using the father's name plus -ovich or -yevich for boys and -ovna or -yevna for girls. So if a father's name was Andrei, than his son's second patronymic name would be Andreyevich and his daughter's second patronymic name would be Andreyevna (you remove the I). Note: These are not a Russian's middle names, they do not have middle names.

And finally the child's third name is his last name, say Smirnov.

Later: VT_hawkeye and Byzantine pointed out several errors, some of which I corrected above. Also, VT_hawkeye pointed out, "if the father's name ends in a short-i (i-kratkoye)," you should use the yevich or yevna suffix.

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Here is a full example:

               Saint name     father's name+suffix     Last name
                      |                              |                                   |
                      v                             v                                  v
  (son)         Ivan               Andreyevich                Smirnov
  (daughter) Anna              Andreyevna                Smirnov
  (father)     Andrei

The phrase in the bonobo's writeup is actually translated as:
"(What is) your first name, patronym?"

Such a pair is the polite/respectful form of referring, often applied to elders. Official papers always require the otchestvo, too. For immigrants who haven't been subjected to this concept before, the patronym is also constructed from the father's name (or what it's thought to might be), which leads to oddities e.g. Irina Mutsuovna Hakamada (which tells us that the political lady's father is Mutsuo Hakamada, of Japanese origin).

Otchestvo used solely can serve as an informal, familiar addressing to aged (esp. rural) people. Kak delá, Petróvich?

Also worth noting that the patronymical suffixes have somehow swapped their etymology with the ones of last names. -ovich|-ovna used to mean rather "descendant of", like in the Rurikovich dynasty; at the Peter I's time, the suffixes were -ov(a)|-ev(a)|-in(a), meaning "belonging to, begotten by", often explicitly appended by the filiation-expressing noun, e.g. Alexey Mikhailov syn. This happened to persist in today's last names, which apparently started off as "transitive" patronyms, not entirely unlike their Scandinavian and English counterparts.