First, Russian middle names always are father's names, patronyms. Women keep their middle name after the marriage while their last name (family name) is changed as usual.
In Russian, patronyms for men always end in -ICH and for women - in -NA. For a given male name, the father's name, a pair of such patronyms (in -ICH and -NA) exists. For some names, short form are also available.
I mean Russian patronyms, these are not used in West and South Slavic countries, however.
Ivayla has already given some examples. Here is one more for names in a-declension:
Father Nikita: Nikitich, Nikitichna.
Assignining patronyms as middle names is obligatory in Russia. Hence, even non-Russian father's name should have a pair of patronyms: