the Russians do something similar, with your middle name being derived from your parent’s first name, but with last names being inherited from the father.
My dad had his dad’s name as a middle name, I have my dad’s as my middle, and my son has mine - but we ain’t commies! It is pretty odd (to me anyway) how they keep track of things what with changing last names and all. Although I guess back in the days of the Soviet Union that may have been a good thing!
It's not actually a "middle name," though it comes between the first and surname.
You are referring to the so-called "patronym" (i.e. "father's name").
Thus, the full name of Anna, the daughter of Ivan Kerensky Sr., would be (until marriage) Anna Ivanova Kerenskaya. Her brother, Ivan Jr., would have the full name Ivan Ivanovitch Kerensky.
Those full names would be the ones appearing in their official papers, but one is hardly ever called by one's full name. Rather, it is considered polite and respectful to use the first name AND patronym (but not the surname) in addressing another person with whom one is not (yet) on a first-name basis. Honorifics and titles like "Professor" or "Colonel" are then dropped. Only in adversarial and confrontational situations would one be addressed only by the surname.
Regards,
in Russian “-ova” means daughter of, ivich mean son of.