I would say for -ов, -ова a closer analogy (grammatically speaking) would be surnames like Jones, Peters (in the sense that they refer to Jone's, Peter's children. An obsolete Russian form would be Иванов сын - son of Ivan, hence the modern surname Иванов, where it kind of lost its original son part). It just happens that -son names are popular in Germanic languages, while -ов is very popular in Russian. That's why it may be perceived as an equivalent.
As for patronymics, the correct forms (depending of the stem) are -ович/-евич/-ич (male), -овна/-евна/-ична/-инична (female) - e.g. Петрович, Петровна. In modern Russian, these forms derive directly from the father's name (interestingly enough, even if the father is unknown or has a non-Russian name, some patronymic will be used in their passport, maybe with some rare exceptions), so the name of the father is clear from them. I wouldn't say it's full equivalent of -son, because the name ending in -son says nothing about the father, whereas the Russian patronymic does.