As long as I have been around and aware of Live Oak, it’s been “Live Oak”… maybe add “Stud”, depending on which part of the very large (and diverse) farm you are talking about and add “International” for the annual event. But on every commercial facing and farm road signage it’s “Live Oak” complete with a picture of a … you guessed it… Live Oak (two guesses on what is found on every square inch of the property). Nobody is competing in an event that is as problematically named as PF (and best as I can tell, no one was asking PF the venue to change it’s name, but rather PF the event). Honestly I do not EVER remember it going by anything but LOS (and LOI) and between growing up in Florida, competing in combined driving and working at racing/breeding farms, Live Oak was somewhat positioned to be on my radar!
Which is all by way of saying it appears Live Oak ditched the plantation portion of the name a very long time ago for a great many aspects of their activities. The original farm name has some historical connections to racing, it was originally founded by P.A.B. Widener, Joseph Widener’s grandson (aka Widener Handicap, owned Belmont, founded Hialeah Racetrack). Maybe the decision to keep the original historical name upon acquisition in '95 was also accompanied by a decision to rebrand as LO and let the back half of the name slip quietly away…