The answer to that riddle is Silence.
From Life is Beautiful by Roberto Benigni (courtesy of GradeSaver.com):
Guido reenters the ballroom, and Ferruccio comes running up to him to tell him that Dora is there. Guido says that he wishes to surprise her, but he hides when he sees Amico coming towards her.
Doctor Lessing is also there, and he tells Guido that he has to leave for Berlin immediately. He says that he truly enjoyed his time with Guido, the most ingenious waiter he has ever come across.
With one final riddle ("If you say my name, I'm not there anymore. What am I?") the doctor leaves. "Silence!" declares Guido to the concierge. "If you say the word, it's not there anymore. Silence. Beautiful."
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