I don't think that'd be legal in the US. Employer has to at least verify that the person is allowed to work in the US (i.e. a citizen, permanent resident, or a legal alien with some work visa) which requires revealing employee's true identity to HR. Or do you think there is a way to perform this (and other tax regulations) without HR knowing the identity of the person?
The employee happens to be the sole owner of Proglonox, but IBM never needs to know the details about that.
In general if the government gets their cut, they don't care about shell games. It's only when using them to hide from them that they get interested.
But what if you were intending to build something more like Silk Road - a business, but with no identifiable legal entities involved? And avoiding prosecution not by following the law, but by being unidentifiable?
I can say I was nervous enough about the whole picture to decline some work some years back, because the person wanted to pay in crypto and I felt like it would get me in for tax complications even though I was willing to do all necessary reporting. The person was outside the US, so some parts of US employment rules wouldn't have applied. I didn't know the other person's name and I don't think he knew mine. Neither one of us was being cloak and dagger afaict, but we had met online and the question simply didn't come up.
Have an example, besides jobs that are completely in-person and pay is done in cash/without government reporting?
Maybe "Sifu" of DeFi protocol Wonderland[0], or "UmbralUpsilon" of Indexed Finance[1], to take just a couple of examples.
Basically, they kept as low as possible the number of people who knew their real identity. That person or persons would verify employment and file the appropriate paperwork.