It's important if you're hiring someone to do something important and you want to verify the owners haven't been named in any other lawsuits, don't have a conflict of interest, etc.
In such case, why not simply ask who the owner(s) are, and/or include such conditions in the contractual negotiations? If the company is not new, there will generally be sufficient information available out there about them. If they are new, then you have every reason (and the leverage) to be particular inquisitive during your due diligence.
Hahah indeed, but having minimum information requirements and penalties in the contract for breach makes this all, more or less, academic IMO.
The point I'm making overall is that demanding there be no anonymity is asking everybody to give up an exceptionally valuable freedom, and what we're getting in return just ranges between nothing for the overwhelming majority of the population, to things with relatively easy solutions for the small percent of people that are affected.
Going with a brand new company without any reputation is always a major risk for anything that matters, and generally not one I'd be willing to take. You act like you're being forced to do business with brand new completely anonymous companies. It's a choice.
As for lying, this is why you have contracts, and in those contracts you have penalties above and beyond losses as penalties. Incidentally it would also generally be a crime. Fraudulent representation of ownership or identity would certainly be prosecutable as fraud and likely other charges. If any money changes hands, you're also setting the stage for wire fraud charges which are particularly nasty, and what really packs on the decades for basically every white collar conviction.
