Presumably it evolved from the honorific format of of 'Mr./Ms./Mrs. Surname', which itself presumably arose out of the societal and familial norms of inheritances and marriage and even profession ("Schumaker" family making shoes, "Baker" family in kitchen work and baking bread, etc.), which surnames historically served as connections and indicators of, while being less commonly shared between other families as first names. Which I would assume was an evolution from systems of tribal clan names into new material conditions.

It's not only a US thing, and not even only English it's a wider west European thing from their particular historical developments and how languages reflected and were reflected in that. In french you have 'Monsieur/mademoiselle surname' too for instance, or Señor/Señora Surname in Spanish etc. etc. And due to surnames indicating profession/status/inheritance/marriage there are also honorifics that were used in that same format for royal and nobility and clergy titles indicating what noble or royal family. "Father Surname"/"Lord Surname"/"Monsignor Surname"/"Monseigneur Surname" etc.