>Ok, that makes more sense. So, the family name (or surname or here in the U.S. lastname) would be 'Ivanov' and if someone had a lastname of Ivanova, they would know that she came from the family of Ivanov? (Or would the 'root' surname be Ivan?) I've seen many languages where words are gender specific (French, Spanish, et al), but not family names.
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The root of this last name is certainly Ivan, but no, it doesn't mean they are all descendants of "Ivan" though may be :)

We do have some Adamov/Adamova as well, though not this common. So, does it mean they do know their beginning? :)

Last names in Russian language are gender specific unless they are foreign, as I said. There are lots of rules how to use them depending on the (hmm, what's the English word "padezh"? - proposition)?

They usually have endings of OV-OVA or IJ/AJA, etc.