In today's Russia, names consist of
a Given Name (imia)
a Patronymic name (otchestvo) and
a Surname (familia)

Given Name

In general there are two types of given names in Russia. There are so-called "Christian" or "Canonical" names which are of Biblical origin. Also, there are the "Old Russian" names which can be traced back to the Vikings or earlier peoples of the steppes
After Russia adopted Christianity in 988, most Russians used "Christian" names

Patronymic Name

One of the earliest ways of differentiating one person from another with the same name was with the use of a Patronymic name
This name is a derivative of the fathers Surname and means either "son of" or "Daughter of"

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Surname

Most surnames in use are, in fact, patronymics that are treated as surnames, i.e., what we now consider to be surnames were, in fact, only patronymics during the pre-1600 period
However, there are some Surnames that are true Surnames but it is often difficult to differentiate between the two

You can read more about the subject of Russian names by visiting;-

Paul Goldschmidt's Dictionary of Russian Names - Grammar