Russian people received their last names (surnames) 100 years ago. It was during the first population census in 1897. Till this time last name was widespread in villages as nicknames.
Then during the population census last names (surnames) was given after father’s names. For example, if father’s name was Peter, then the last name (surname) was Petrov (it is form of word Peter which is answer the question “whose you are?”). That is why the most widespread Russian last names:
Ivanov, Petrov, Vasiliev, Nikitin, Tarasov, Titov, Fedoseev, Fedorov, Sidorov, Alekseev, Egorov, Demidov, Mihailov, Andreev, Alexandrov.
In Russia women usually adopt the surname of their husband. Most of Russian last names ending change depending on gender, for example, male – Ivanov, but female – Ivanova. In most cases ending “a” is added in female last names. Petrov – Petrova, Eltsin – Eltsina, Gorbachov – Gorbachova, Putin – Putina. There are some disputes about translation of Russian female last names, for example, last name Gorbachova can be translated as Gorbachov and Gorbachova. Variant Gorbachov is the most widespread.