As someone who has written academic papers about the role of disguise and deceit in the Odyssey — Nobody is so damn important.
Prior to this point, when Odysseus tries to exercise Xenia (ancient Greek guest rites/hospitality code), he did what he was supposed to do. (Well, we think so anyway — notably, the most famous books of the Odyssey are told by Odysseus, who isn’t exactly a reliable narrator.)
But when Polyphemus kills and eats some of the men, the game changes. The Cyclops makes it clear he has no intention of abiding by Zeus’s laws, and will cannibalize the lot of the men. So, Odysseus responds in kind — he breaks Xenia and lies. He introduces himself under a false name as part of a trick. Polyphemus then breaks Xenia again — he tells Nobody he’ll be eaten last, and that is the Cyclops’ guest gift to him.
Odysseus’ transgression is clearly the lesser one. The Nobody trick works. It gets Odysseus and most of his crew out of the cave alive.
But, crucially, before leaving Odysseus sheds his disguise. He admits his true identity, in detail, so he can boast of his achievements and add vanquishing a Cyclops to the list. And it bites him in the ass spectacularly.
The only reason why Polyphemus can curse Odysseus, can bid his father Poseidon to curse the man who blinded him, is because he now knows who did it. If Odysseus had kept his mouth shut, he might have safely made it home from there. But while a big part of why the Nobody disguise vs. real name reveal is showing Odysseus’s hubris, it’s not just about that. It’s also about the start of a pattern that hurts him more than it helps him.
From this point in the Odyssey on, Odysseus lies about his identity constantly. And sometimes it protects him, but more often it’s a detriment or at least unnecessary. He’s lying about his identity primarily to people who are on his side — a kindly loyal swineherd, his son, his faithful wife, his ailing father.
The last one is especially damning, because happens when Odysseus has already killed the suitors and returned home and reunited with the rest of his family sans disguises. He knows from everyone else that Laertes never betrayed him or his legacy, but was mourning his son and heartbroken for almost a decade. Odysseus has publicly declared his return to everyone else — his father doesn’t know because he’s living in squalor remotely. But Odysseus doesn’t tell his father who he is. He makes up a fake identity and tells a story implying Laertes’ son is dead. And when Laertes bursts out crying, then Odysseus drops the charade and finally admits who he really was.
There was no utility to that lie. No loyalty to test. No hidden threats to worry about. But Odysseus still instinctively lies to his beloved father about who he is, only dropping the charade when he sees the damage it’s doing to his relationships.
Because at this point, lying is pathological for Odysseus. He can’t seem to stop doing it. Because with Polyphemus, a lie protected him and the truth hurt him. That is the point of the “ Nobody” disguise.
And they fucking cut it???