In May 2022, the chief financial officer of Boar’s Head, the processed meat company, was asked a simple question under oath.

“Who is the C.E.O. of Boar’s Head?”

“I’m not sure,” he replied.

“Who do you believe to be the C.E.O. of Boar’s Head?” the lawyer persisted.

The executive, Steve Kourelakos, who had worked at the company for more than two decades and was being deposed in a lawsuit between owners, repeated his answer: “I’m not sure.”

It is odd, to say the least, when a top executive of a company claims not to know who his boss is. And Boar’s Head is no fly-by-night enterprise. The company is one of the country’s most recognizable deli-meat brands; it generates what employees and others estimate as roughly $3 billion in annual revenue and employs thousands of people.

But anonymity and secrecy have been central features of Boar’s Head, a privately owned company run by two intensely guarded families, the Brunckhorsts and the Bischoffs.

“They’re as secretive as anybody I can think of in the industry,” said Tom Johnston, the editor of Meatingplace, a trade publication for meat processors.