To me, it seems the only way to enforce this is to invoke some sort of KYC mandate for social media sites. Obviously, in practice this would only target legitimate companies. So yeah, I think you would simply need to require that people verify their accounts in the same manner that say a Cryptocurrency exchange verifies a person. In such a universe Elon Musk might finally gets all his users to buy a blue mark.
Such regulations would drive me to use only foreign-owned shady companies who do not care about US law. I'd be sure to spread the word to my fellow citizens.