Why do you think Odysseus wants Polyphemus to know who blinded him?
Odysseus wants Polyphemus to know who blinded him because of his immense pride. Polyphemus has ignored the religious imperative to offer hospitality to strangers, instead choosing to eat several of Odysseus's crew because he believes himself to be more powerful than the gods. It is actually Polyphemus's pride that renders him so abhorrent to Odysseus. As his ship sails away, Odysseus shouts back to shore,
"Cyclops, in the end it was no weak man’s companions you were to eat by violence and force in your hollow cave, and your evil deeds were to catch up with you, and be too strong for you, hard one, who dared to eat your own guests in your own house, so Zeus and the rest of the gods have punished you." (9.475-479)
Odysseus really wants to rub it in that Polyphemus is not as strong as he thinks and that Zeus and the gods have permitted him to wound the Cyclops as punishment for his terrible pride. But the quality that prompts Odysseus to name himself as "no weak [man]" is his own pride. And despite the danger the monster still posed to them (via his own strength and because Poseidon is his father), Odysseus continues, "'Cyclops, if any mortal man ever asks you who it was that inflicted upon your eye this shameful blinding, tell him that you were blinded by Odysseus, sacker of cities." Odysseus very much wants the monster to know the name of the man who bested him. This can only be the result of his own pride which is so immense that it overcomes any concern for his or his crew's well-being.