Russian Names (2018)

Moving to a Western country and having a Polish name with a fixed diminutive effectively means having two different names, each one used with different crowds. Work colleagues know me by my full name, everyone else by the diminutive. A friend of mine who is seeking naturalization pondered simply assuming the diminutive as her official name for simplicity, because it's how she introduces herself to everyone.

In my home country people have the diminutives encoded and they know to switch when we are in an informal context. Full names are rarely used in speech if one's name has a diminutive - if you don't know someone it's more likely that you will only use Mr/Mrs + their last name, otherwise you address them with a diminutive. A curious intermediate form of address is found in superiors at work and people who met as older adults - Mr/Mrs + first name, which then can be a diminutive or not depending on personal preference.

    I think that the most common Russian male name is Sasha (Alexandr)…

What is the relationship between the two names? I've known multiple people named Alex, but never met a Sasha in person. Is Alex/Alexander a nickname for Sasha, like Chuy is for Jesús, in Mexico?