I’m not sure what you mean by “signify family” as the name itself is what most often signifies a person’s family. 
  
However, some common prefixes are De- for Italian names or Mac- for Celtic names. For example, the names DeLuca and MacArthur use these prefixes.   

Some common suffixes might be -er as in Fletcher or -son as in Johnson. Suffixes are often added to indicate a person’s affiliation with the root word. For example, Fletcher indicates a person’s family came from the profession of making arrows, or the name Baker indicates that person’s family came from the baking profession. The suffix -son in Johnson indicates that a person’s family descended from an ancestor who’s first name was John.
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