It's called a patronymic -- it's used in formal address and if you read Dostoyevsky or Tolstoy you'll hear the characters always use the patronymic with each ot

It's called a patronymic -- it's used in formal address and if you read Dostoyevsky or Tolstoy you'll hear the characters always use the patronymic with each other if they have a formal relationship. They'll say "Sofia Semyonovna" every single time, not just once. You can't say it's a "middle name" or a "second last name" really, it's its own thing.