Among the nobles in Russia, surnames first appeared in approximately the 13th century. It was not until the 17th century that peasants began receiving their surnames. The mandatory documentation of surnames began after the October revolution of 1918. There are multiple sources of surnames: old ancient names, nicknames, trades and occupation, personal characteristics, appearance and location (e.g. Жданов - expected, Третьякова – the third, Бобров - beaver, Зайцева - hare, Кузнецов - blacksmith, Попова - priest, Худоногов – thinly-legged, Бездомникова - homeless, Лесной - forest). Sometimes surnames combined two sources of derivation and were hyphened (e.g. Мамин-Сибиряк, Панкратов-Чёрный – Mamin-Sibiriak, Pankratov-Chernyi)

The most common indigenous Russian surnames have the following endings:
"–ов/-ова", "-ев/ева", "-ёв/ёва" (–ov/-ova, -ev/eva, -iov/iova). Example: Львов (Lvov), Синяева (Saniayeva), Кушнарёва (Kushnariova)
"–ин/ина", "-ын/ына" (-in/ina, -yn/yna) Example: Фомин (Fomin), Лисицын (Lisitsyn)
-ский/ская, -цкий/цкая (-skiy/skaya, tskiy/tskaya) Example: Рождественская (Rozhdestvenskaya), Высоцкий (Vysotskiy)
-ой/ая (-oy/aya) Example: Толстой (Tolstoy); seldomly: –их/-х (-ikh/-kh) Example: Каменских (Kamenskikh);
and more seldomly surnames with zero ending. Example: Воробей (Vorobey).

Surnames are often used in formal communication and are usually preceded by "господин" (Mr.) or "госпожа" (Mrs.): господин Харитонов (Mr. Kharitonov), госпожа Хрусталёва (Mrs. Khrustaliova).

A sole surname is often used in educational institutions to address students or when discussing a famous person. In other cases the usage of a sole surname is impolite and even rude: Ребров, Корольова – Rebrov, Koroliova.

The threefold form of a name (name, patronymic and surname) is formal. It is used to mention a respected person or present them to an audience: Александр Сергеевич Пушкин – Aleksandr Sergeevich Pushkin.

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Source: russianlessons.net