One way of obtaining a limited amount of further information is to click on the info button to the left of HTTPS in a website's URL. Of course, you may not wish to visit a booby-trapped website, but if you are already there, and want to check bona fides, then try it.
In many cases you will see "no ownership information", but sometimes clicking the details button gives an inkling as to ownership. If you do this on, for example, the BBC website you will see the owner is British Broadcasting Corporation.
So, very hit and miss, but until ICANN get their finger out (or whoever it is that's supposed to give us this info - Companies House can do it for companies, so it's not impossible), this is arguably one way to check ownership of a domain.
For someone wishing to be proactive about identifying themselves and their business as genuine, this could be a good way for them to do so in the absence of WhoIs. Buy a certificate which enables ownership information to be embedded.
On the downside, there are a lot of dodgy certificate-issuers out there.