The original title of the organization was the Intercollegiate Society of Individualists. This was originally the vision of Frank Chodorov. You can find information on the early history here, here and here.
When I joined ISI in 1968, it had already been converted into a conservative organization and was rapidly shedding its libertarian principles for Burkean conservativism and had already changed its name from the Intercollegiate Society of Individualists. It was disappointing in that respect, but there were still enough libertarian elements in it for me to continue with it for some time.
Just a thought.