Answer:
Odysseus reveals his name to Polyphemus, the Cyclops, out of pride and hubris. After blinding Polyphemus to escape captivity, Odysseus cannot resist boasting about his identity.
However, this act of arrogance puts his men in more danger as Polyphemus, being Poseidon's son, calls upon his father to curse Odysseus and his crew. This leads to a perilous journey home, as Poseidon's wrath causes numerous hardships and delays, prolonging Odysseus' return to Ithaca.
Odysseus' prideful decision to reveal his name and taunt Polyphemus becomes a pivotal event that significantly impacts the challenges he and his men face on their voyage back home.