He enjoyed life under the Florida sun until authorities nearly discovered he was undocumented, and he boarded a bus that arrived in New York one snowy afternoon in 1964. “I had a different name each week afterwards,” he said. “I was Oscar. Then I was Ray. At my job office the guy said, ‘Hey, weren’t you Ray yesterday?’ I told him, ‘Yes. I am both.’” Mr. Alvarez finally became a waiter and settled into a cramped apartment in Alphabet City. When he heard that a local candy shop was for sale, he made an offer for it, inspired to become his own boss.