The registrar is public, the contact details usually are not. A lookup tells you which registrar holds the domain, when it was registered and when it renews. Privacy protection masks the registrant name and address, which is now the default at most registrars.
The question behind the question
Usually this is not really about ownership. It is a business discovering that nobody currently employed can log in to the registrar, because the domain was registered years ago by a web designer, a contractor or someone who has left.
Knowing the registrar is the first step. The second is finding the account, which means checking every business address ever used.
If the account is not yours
Start the recovery process with the registrar directly, using evidence that the business is the rightful owner: incorporation documents, trademark records, historic invoices for the domain. It varies by registrar and takes weeks.
Start it before there is a deadline attached. Recovering a domain is far easier while the relationship is merely ended than after it has turned adversarial.
One extension where more is public
For .co.uk, Nominet records the registrant separately from the registrar, which means you can see and update ownership through Nominet rather than only through whoever holds the account.
This is the short version. The full guide covers it properly: read more.