designation vs family name

designation

noun
  • That which designates; a distinguishing mark or name; distinctive title; appellation. 

  • Selection and appointment for a purpose or office; allotment; direction. 

  • signification, meaning, for example of a word or phrase. 

  • An act or instance of designating; a pointing out or showing; indication. 

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. 

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