False.
Issur Danielovitch was his birth name.
Not false.
Douglas was born Issur Danielovitch in Amsterdam, New York, the son of Bryna “Bertha” (née Sanglel) and Herschel “Harry” Danielovitch, a businessman.[3] His parents were Jewish immigrants from Gomel (now in Belarus but then in Russia),[4][5] and the family spoke Yiddish.[6][7] His father’s brother, who emigrated earlier, used the surname Demsky, which Douglas’ family adopted in the United States.[2] In addition to their surname, his parents also changed their given names to Harry and Bertha.
His 1988 biography paints a memorable picture of his family in the early years in America. After noting that his father was denied work in the carpet mills, the town’s largest employers, because he was Jewish, Douglas writes:
So my father, who had been a horse trader in Russia, got himself a horse and a small wagon, and became a ragman, buying old rags, pieces of metal, and junk for pennies, nickels, and dimes. . . . Even on Eagle Street, in the poorest section of town, where all the families were struggling, the ragman was on the lowest rung on the ladder. And I was the ragman’s son.
Douglas grew up as Izzy Demsky and legally changed his name to Kirk Douglas before entering the Navy during World War II.[8]
http://en.wikipedia.org/wiki/Kirk_Douglas