If somebody works hard at a working class job, enough to become their own boss by either e.g. starting their own cleaning company, or buying another business li

If somebody works hard at a working class job, enough to become their own boss by either e.g. starting their own cleaning company, or buying another business like a hotel that they cleaned - are they no longer working class? Can they no longer claim to be of working class background? This seems absurd to me. They were not born into money. They had to work hard to get to where they were.