In the old days Johnson might've meant literally "son of John" but no longer. All of the people with the surname "Ivanov(a)" on that page also have a patronym, which in the West would be considered a middle name.
Referring with surname only is a hierarchy assertion thing, and somewhat rude - boss would talk down to subordinate like that, or teacher to student. When talking "up" or "sideways", or "down" but without a desire to assert superiority a name+patronymic is usually used, which reflects a respectful distance while not slipping into rudeness or overt familiarity. Sadly, it is mostly disappearing and giving way to Western "name-only".
And then, to emphasize familiarity, some groups adopt way of referring to each other by patronymic only :)
Generally, -vich suffix is used in masculine form and -vna suffix in feminine form.
In high school, we referred to our teachers by honorific and surname, and we were also addressed by surname, even by our peers.
When I rewatched the Harry Potter film series this year, I began paying attention to how Harry was addressed. Draco Malfoy called him "Potter". So did many teachers, "Mr Potter". He who must not be named called him "Harry" and many epithets like "the boy who lived". Hagrid and Professor Dumbledore, at least in private, called him "Harry" all the time.
This is especially interesting, because "Potter" is a homophone with the Latin Pater, meaning "Father".
That said, I don't speak Russian and have only a passing familiarity with the construction of Russian names, so don't take this as gospel.