Why John von Neumann is not known as a synonym for "genius" given his accomplishments?

So, it's hard to answer why something didn't happen. It's much easier to answer questions like "Why did Albert Einstein and Isaac Newton become synonymous with 'genius'?" In both of those cases (which you can find more complete answers on here if you search), the act of making them famous was both a result of their accomplishments (both impressive) and the "role" they ended up playing the culture that lauded them.

So for Einstein, his fame initially was as the "obscure German-Jewish physicist who overturned Newton" (which itself was made a huge deal of by Sir Arthur Eddington because he believed it would help "heal the wounds" of World War II — a British Quaker proving the theory of a German Jew), and then became permanently "famous" when he became a symbol of "what happens when you think some abstract theory doesn't matter, and then someone makes an atomic bomb (somewhat) based on it." And for Newton, he became a rallying-cry for the later Enlightenment (to a whitewashed degree that actually obscured at a lot of his historical activities), a model of what an idealized "scientific" mind could achieve (ignoring all of the "non-ideal" stuff he spent the majority of his time on, like theology and alchemy). Which is to say, both became famous beyond their respective communities of expertise because their fame played a "role" in a broader social context. They became, in other words, symbols. Stephen Hawking is another, outsized example of this: most people could not tell you what his scientific contributions actually even were, even in popularized form — whereas they can say "E=mc^2 " for Einstein and "discovered gravity" for Newton, even though both of those answers actually are pretty wrong in different ways. What they know about Hawking is that he was the genius scientist who was confined to a wheelchair and talked through a machine, the ultimate poetic demonstration of the mind-body problem.

But anyway. Back to von Neumann. John von Neumann made a lot of fundamental contributions. The importance of some of them were known in his time, though his contributions to quantum physics were (and still are) pretty obscure to non-experts, his contributions to nuclear weapons were highly classified until after his death, and his contributions to modern computing were so far ahead of their time that their impact could only be glimpsed at. He died relatively young. He never did any kind of serious science popularization or public outreach (other than his government service as a member of the Atomic Energy Commission). He is the kind of person you know about if you care about these kinds of scientists but his public profile is and was comparatively low, at least relative to many of his other contemporaries (Oppenheimer, Bohr, Fermi, and even Teller were far more famous).

To be sure, he was regarded as a great genius by his contemporaries, and as a result there has been a lot of acknowledgment of that, especially in the years after his death. But he doesn't really play a "role" in our culture, you're right. It may not have helped that his politics were pretty right wing, and he was a notorious "hawk" when it came to nuclear weapons. (But not as eccentric as his fellow Hungarian, Edward Teller, who also did a lot of public outreach and was the center of a lot of public controversy.)

So the idea I would leave you with is that who we associate with "genius" is not just about how smart people were or how important their contributions were. There have been a lot of smart people in history who have made some pretty big contributions but are totally obscure, even more so than von Neumann. (One of my favorite things to ask physicists and historians is: who is the ONLY person to have won two Nobel Prizes in Physics? Pretty much nobody knows. And for a lot of people, even if I tell them the name — >!John Bardeen!< — it doesn't ring any bells. >!He won the first for the transistor, the second for superconductivity. Both pretty big!!< But he was, as one of his biographers wrote, a very un-eccentric person, and he doesn't make for an exciting story, so he's not one of the luminaries we talk about much.) In order for someone to transcend the fame of their own expert community, it takes more than that. (Murray Gell-Mann was extremely irritated that his Caltech colleague, Richard Feynman, was far more famous than he was even though Gell-Mann arguably produced the more impactful scientific work. Gell-Mann tried to emulate Feynman's "storytelling" abilities but never could pull it off.)

To become that famous, as a scientist, is an unusual thing, and in every case where it has happened, one can usually identify (at least with hindsight) what "boxes" the scientist was ticking culturally. It's hard to say for certain why von Neumann didn't tick those boxes, but I suspect the classification of his work played a role in it.