What makes you say he "didn't realize" what else was in America at the time -- other than what was obvious? I suspect you have no basis for saying that and are guessing. He may have "realized" or may not have, or more likely didn't care. He just started teaching what he was taught, or what he knew, or what he could, or what he chose to. And called it at first what everyone else was calling everything else -- to the extent anyone was public with it what they were doing at all: "karate."
I'm sure there were private, maybe even underground schools, teaching only to ethnic Chinese and in Chinese communities (at least that's what Bruce Lee's bio-pic said he got in trouble for breaching). And they may well have told their students it was Hung Gar, or CLF, or Shaolin, or who knows what. Maybe didn't call it anything. But I'll bet a lot of them didn't even use the term "kung fu" until much later. But I could be wrong.