He wanted to know Odysseus's name so that the Cyclops can cry out and be asked by other Cyclopes if it needs help.
Answer: To prove to Polyphemus that he was the one who defeated him.
Explained: Odysseus slips his name in order to show the Cyclops that he was the one who defeated him. This will later come back to haunt Odysseus when Polyphemus tells his father, Poseidon. Why does Odysseus reveal his name to Polyphemus after he has escaped? To prove to Polyphemus that he was the one who defeated him.
