How many people are actually informed that the Washington Post is owned by Jeff Bezos? How many people know that Jeff Bezos has contracts with the CIA[1] & sits on a pentagon board[2]? I doubt many. It's one of the few "left" wing newspapers I refuse to read for the reasons above.
I'm not arguing for this blockchain solution, I think it makes things worse exactly as you said.
Every time the Washington Post mentions Bezos, or a company he owns, even in the abstract (for instance, in this spaceflight article, which mentions blue origin: https://www.washingtonpost.com/news/business/wp/2018/06/15/f... ), they say that Jeff Bezos owns the washington post, in those exact words.
Given that the President of the United States went on a yelling spree recently about Bezos' ownership, I'd say most people who can distinguish the Washington Post from the Washington Times (owned by Sun Myung Moon's religion and absurdly right-wing) also know who owns the Post.
(Which isn't to say everyone knows that either—a lot of people seem to take the Times equally seriously—but solving the problem of bad-faith media existing is another one entirely, and quite probably the answer is it shouldn't be solved at all.)