Israel ben Eliezer, more commonly known as the Baal Shem Tov (master of the good name) was the founder of Hasidic Judaism. Israel Zangwill was a nineteenth-century British writer, and, fittingly, Zionist. Israel Amter was a cofounder of the Communist Party of the United States. And Israel Aharoni officially named and collected the Syrian hamster, now the most common hamster in the world (all domestic ones, incidentally, are descended from one pair of hamsters).
Israel Gelfand, (1913-2009), famous Russian-American mathematician. With his works including group theory, representation theory, and functional analysis.