Given Name + Patronymic Name + Surname
Given name: Vladimir
Patronymic name: Alexandrovich (son of Alexandr)
Surname: Putin
The patronymic name and surname changes between male and female.
What is not clear is why Igor is not written as Igorevich.
Perhaps a Russian/Ukrainian user can weight in?
Canadian immigration service, for one, just cuts patronymic name if total length of first + patronymic + last names exceeds certain limit (my guess - the limi tis length of the field in some form/database). So "Igorevich" becomes "Igore" or "Igorev" depending on you first/last names lengths. US may have more flexible rules and lets you provide your version of middle name or drop it altogether.
I wouldn't attach too much importance to this detail