So if you're just starting out, put this on your list. Jewish names are mentioned in the complete article.
The first key is to understand the structure. Most Russian full names consist of three parts, just like American ones. The difference is the middle name: whereas Americans tend to select a middle name for the way it rolls off the tongue between the first and last name, or as an opportunity to squeeze in an additional family or saint name, in Russia the middle name nearly always consists of the father's first name.
This is called the patronymic (patro meaning father), and has two components: the father's name, plus an ending that means "of" (as in son or daughter of). These endings usually look like "-ov/ova/ovna", "-ev/eva/evna", or "-ich/ovich/evich". (The versions with an -a at the end would be for the daughter, and the other versions would be for the son).
We can use Vladimir Putin as an example. His full name is Vladimir Vladimirovich Putin. Looking only at the middle name, we see a compound name: Vladimir + "ovich". Thus, his full name is Vladimir -"Son-of-Vladimir"- Putin. Another example is Leo Tolstoy, whose full name is "Lev Nicholaevich Tolstoy". His middle name, Nicholaevich, is the compound of "Nicholai" + "evich", and means "the son of Nicholas."
Melissa includes lists of common formal names (diminutives and nicknames as well) for men and women. Many given names are Biblical, Latin and Greek, as well as Old Slavic.
She discusses the polite way of addressing people, using the given name and patrynomic; addressing close friends or family members with pet names that get longer as the relationship is more intimate.
Example: Andrei Andreyevich (formal), Andrei (casual), Andrushka (very close), Andrushochka or Andrushenka (extremely close).
Sometimes, however, the nickname does not resemble the original name at all. For example, Sasha is the short form for Alexander, Vova for Vladimir.
To satisfy your curiousity, the following are popular nicknames (in parentheses). Anastasia (Nastya), Anatolyi (Tolia, Tolik), Anna (Hanna, Ania), Boris (Borya), Dmitri (Dima, Dimochka), Elizaveta (Liza), Ivan (Vanya, Vanechka), Larisa (Lalya, Lara), Natalia (Natasha), Oleg (Olezhka), Olga (Olya, Lyolya), Pavel (Pasha), Pyotor (Petya), Sergei (Seryozha), Stepan (Styopa), Vadim (Vadik), Vasily (Vasya), and Viktor (Vitya).
Surnames and endings, which tend to be adjectives or like patronymics, are also addressed.
In the adjective category: "Joseph Stalin (born in Georgia with the last name Dzhugashvili), chose his future last name to match the adjective meaning Steel- a choice whose significance was not lost on Soviet citizens."
Professions fall in this category: "The name Boyarsky is derived from the title "Boyarin", meaning landed gentry or nobility."
In the patrynomic category (endings of ov/ev), names are generally male first names, animals, colors or cities of origin: "Chernov contains the root word "Chyor", which means black; Medvedev contains the root word "Medved" which means bear...".
Don't be intimidated, says Melissa, the next time you see a Russian name:
Simply look for the markers- the endings of -y, -sky, -in, -ov/ev, -ovna/evna, and -ich. Sound it out and see if it sounds anything like the names that are already familiar to you. And, if you are especially ambitious, look up the root word to get a sense for the way that the name comes across to Russians. (You don't even need to know the Cyrillic alphabet; you can go to an etymology site in English). At the very least, when you come across a Russian name, you will be a little less lost than before.
Read the complete post at the link above.