One aspect of the Russian language that I have trouble understandin​g is the traditional use of patronymics.​  As you know, in American English, patronymics aren't used at all.  Our traditional name formation is based on the given name (or "first name") and the family name (or "last name").​  Of course, we also add the second name (or "middle"​ name), but we rarely use our middle names (with the exception of individuals that, for one reason or another, use their middle names as their first names - but that isn't common). 

I think that common American English is very informal usually.  We generally refer to each other on a first name basis, and only use the last name in very formal situations, to show respect, or if we don't know what the person's first name is.  I think, though, that nicknames are very common here, perhaps more so than in Russia. 

Nicknames here aren't always based off of what a person's first name is, as they seem to be in Russia.  Instead, they usually combine either some affectionate​ way of saying someone's first name (similar to how it is done in Russia, I think) or is some other name entirely, based on the person's interests, attitudes, or personality.​ 

Occasionally​, we use "baby names" as nicknames.  By that, I mean that often, young children have problems pronouncing their given first name, so they shorten it to something they can say.  For example, my sister's "baby name" was Kiki because she couldn't pronounce her given first name of Kimberly.  Now, Kiki has become her nickname. 

At other times, a person combines the initials of their first name and their middle name to come up with the name they prefer to be referred to as.  Such is the case of people called "BJ"​, or "JR"​.

Another version of the a nickname comes from a deviation of a person's given name.  For example, a person's given name maybe "William", but he may be called "Bill", "Billy", "Will" or "Willy".  Other names like this include "Robert" (shortened to "Bob", "Bobby", "Rob", or "Robby"), Richard (shortened to "Rich", "Rick", or "Dick"), Gerald (shortened and respelled "Jerry"), and Thomas (shortened to "Tom" or "Tommy"). 

There are a few women's names that also behave this way.  For example, "Jacqueline" is often shortened to "Jacky".  Francine (shortened to "Franny", "Fran", or even "Franky"), Kimberly (shortened to "Kim") and Catherine (shortened to "Cathy") are some other examples.

To add more complication, there are generic nicknames that are often used.  Some of these are more common than others, depending on the geographical region you are in.  For example, you may be called "dear", "deary", "hun", "hunny", "sweetheart", "babe", "dude", or "sweetie".  These are also occastional terms of endearment used sometimes, but they are often used in everyday life when refering kindly to someone you don't know. 

Here are two examples of the usage of the word "hunny/honey".  A husband may call his wife "hunny/honey" as a term of endearment for her.  At the same time, a waitress in an informal dining resturaunt may say something like "Can I take your order, hunny/honey?"  The waitress doesn't call a person that as a term of endearment like the husband used, but uses it to make the person feel more at home and comfortable, and is trying to be nice to the person.

Unfortunately, there are no hard-and-fast rules to the giving of nicknames in English, as there are in Russian.  A person may have a given name of "Charles" (the shortened term of which is "Chuck") but want to be called "Joe".  Of couse, you wouldn't know this to begin with.  It usually comes up during the introduction phase of the conversation.  The following is an example.

Person One:  Hello.  Are Mr. Charles Hadden?
Person Two:  Hello, yes, I'm Charles, but call me Joe.
Person One:  Nice to meet you, Joe.  My name is James Clinton, but call me Jim.
Person Two:  Nice to meet you, Jim.

Usually, when introductions are made, the person will either tell you how you should refer to him.  However, when the person is an authority figure (such as a teacher or a boss), it is usually expected to refer to them as Mister (Mr.) or Misses (Mrs.) followed by their family name.  In the situation above, the men would formally be refered to as Mr. Hadden and Mr. Clinton.  American's, however, don't stick to these rules under all circumstances.  We move rapidly from the formal to the informal, often with few clues to non-native speakers as to why that transition was made.  Often a boss will be refered to by those he supervises as his first name.  Sometimes those in a clear position of authorty over another person will refer to him or her as Mr. or Mrs. followed by their family name, but usually only when the person of authority is much younger in age than the person they are talking to.  Finally, some people dislike being refered to as Mr. or Mrs. in any circumstance, but they usually indicate that during the introduction conversation.

The best way to discover how to refer to someone you are meeting for the first time is to get clues or instructions during your introduction.  In an uncertian situation or if meeting for the first time, always greet someone in a formal manner.  If a person wishes you to refer to them regularly in this formal manner, they will NOT correct you during the introductions.  However, if the person wishes you to refer to them in a less formal manner, they will usually say so, as well as tell you exactly what name to use for them.