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.

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