There's some info that you can get to from the BtN homepage about names from different countries. Basically, you just add -ovich (evich) to the father's first name for the sons and -ovna (evna) for the daughters. There are a few names with slightly different patronymics. Iliych and Iliyshina for the children of
Ilya is the only exception I can think of at the moment. If you look up the names of famous Russians/ Soviets you can get some more examples.