Answer: Rudy
Gordon Gekko's son is named Rudy. Gekko mentions his son in several scenes in "Wall Street." Once, for example, Gekko shows Bud Fox a miniature television and says that it's a present for Rudy, the "electronics freak." In another scene, at Gekko's private swimming pool, Gordon exclaims, "Rudy, my gazoudy!" and asks his spoiled three-year-old son to speak French. It will be interesting to see how Rudy Gekko develops as he matures into a young man.