The San Francisco company is part of a generation of hot startups valued in the billions of dollars. But their financial maturity is a concern. Jack Dorsey, Square’s CEO, puts an even greater spotlight on an IPO. He is a well-known Silicon Valley figure who, earlier this week, took on the additional high-profile role as Twitter’s permanent CEO. The decision immediately sparked an intense debate within the tech industry. Could he really effectively manage two companies simultaneously? Square’s path to an IPO started this summer, when it submitted a confidential filing to federal regulators under the JOBS Act, an option...