Jake Dyson has a vision for the future of his family’s $9.5 billion company

When Jake Dyson looks back at his childhood, he doesn’t remember his father, James, as the visionary founder of Dyson, the world-renowned technology brand. Instead, he recalls a tinkerer who was always working on something in the basement. “I watched Dad being a bit of a crazy inventor,” the younger Dyson says. “He was mucking about with potato peelers, amphibious vehicles, boat trolleys . . . all sorts of ideas on our doorstep.” James’s inventive streak paid off. In the late 1980s,...