Looks like that was the full version of the acronym for most of TOS
USS was referred to as standing for either “United Space Ship” (TOS: “The Cage”, “The Menagerie, Part I”, “Space Seed”, “The Gamesters of Triskelion”, “Patterns of Force”, “Assignment: Earth”, “Elaan of Troyius”) or “United Star Ship.” (TOS: “The Squire of Gothos”, “Court Martial”)
Looks like that was the full version of the acronym for most of TOS
https://memory-alpha.fandom.com/wiki/USS