family name vs middle name

family name

noun
  • A given name common in a family, or already borne by someone in the family (in the context of naming someone in the family after that family member). 

  • A surname. 

middle name

noun
  • A name between the first given name and the family name or surname; a second or subsequent given name. 

  • A trait, activity, or action closely associated with or aptly describing a person. 

  • One's mother's maiden name. 

How often have the words family name and middle name occurred in a corpus of books? (source: Google Ngram Viewer )