Is this part of The Cyclops of Homer’s Odyssey? If so, Odysseus most likely revealed his name so that Poseidon would know that him and his crew had harmed his son (Polyphemus, the cyclops) and weren’t beaten down by Polyphemus. When Odysseus started screaming stuff at Polyphemus like his name and all, his crew told him to stop since Polyphemus had recently broke off a piece of a mountain and threw it at his ship (meaning that he was extremely powerful and could very well destroy them).