>I understand gender specific firstnames, but not surnames. What surname do the children take on then? How does a surname get passed from generation to generation?
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Children get their father's surname (it's called here initial, though kids here don't inherit father's name).

E.g.

Last Name     First Name        Surname         Gender  
Ivanov        Ivan              Ivanovich       male
Ivanova       Ol'ga             Ivanovna        female