We can't really answer why you haven't heard of Oppenheimer. He is certainly not systematically excluded. However it is worth noting that Oppenheimer's scientific contributions were rather limited compared to Einstein's. Oppenheimer's fame came from his work on the Manhattan Project, which was his major life accomplishment. Prior to that his work as a physicist was very promising, but he never stuck with a given topic long enough to fully develop it. Had he done so, he probably would be known for far more in physics — work he did eventually led to people discovering black holes, for example. Even that would not put him on Einstein's level, though — Einstein re-wrote modern physics.

It is somewhat ironic, and has been noted by scholars before, that the one time in Oppenheimer's life that he really followed something all the way through was when the entire weight of the US Army and the federal government was forcing him to do it. Even then he had many self-doubts and even volunteered to resign at one point.

None of this takes away from Oppenheimer, but his scientific achievements on not on par with Einstein, Bohr, Heisenberg, etc. He is another level down. It is an interesting thing to note in part because nobody doubted his intelligence — the issue appears to have been his approach to science, which was not persistent-enough to develop the true breakthroughs that are required (going a bit against the traditional views of what "genius" tends to mean). His historical achievements are quite high, though, but that is because of his work with the government and for the military. He is certainly present in any discussion on the history of nuclear weapons, and far more important than Einstein in that arena (Einstein gets more credit than he really deserves when it comes to nukes).