Oden's journal contains a prophecy about how strong pirates will enter the New World and help take down Kaido. Yamato appears to be having an identity crisis, spouting off seemingly inconsistent lines left and right. However, Yamato has not once denied their birth name; what Yamato doesn't understand is who plays what role in the prophecy. As the story is unfolding, Yamato is actually trying to understand what's happening in the context of the prophecy, and we can understand everything they've said by stepping through chronologically with this in mind.
- Finding the journal: Yamato witnesses the death of Oden, and believes his family and all of his retainers are also dead. Upon finding the journal, Yamato learns that Oden was supposed to open Wano for Joyboy's arrival. Yamato begins to think of "Oden" as the one who fulfills the prophecy in the journal: a free man that helps strong pirates overcome Kaido and open Wano. Yamato thinks that they're the only one that knows this, and resolves to fulfill the prophecy and "become Oden".
- Meeting Ace: Yamato meets Ace, and doesn't mention becoming "Oden" once. After all, nobody needs to be "Oden" until the time of the prophecy. However, Yamato does form a close connection with Ace, and learns all about Luffy.
- Meeting Luffy: Yamato introduces themselves to Luffy, saying "I've been waiting for you! I'm Yamato, Kaido's son!" We're meant to think that this is "Oden" waiting for Joyboy, the one from the prophecy. However, Yamato is not sure which if any of the invading pirates is Joyboy. Instead, they seek out the one they do know: Luffy, Ace's brother. We know that Luffy is the one Yamato is waiting for from the titles of Chapters 999-1000: "The sake I brewed while waiting for you", "Straw Hat Luffy". Yamato even uses the name and title which Ace knew, in the off chance that Ace mentioned Yamato to Luffy.
- Attic conversation: Yamato explains to Luffy that since the Akazaya Samurai are dead, "someone has to carry on Oden's will", so they will do it. When Luffy questions this, Yamato reacts by trying to apply the prophecy: maybe Luffy is the free man that will help open Wano, or "more Oden than me".
- Learning that Momonosuke lives: One of the last things that Oden said before he entered the boiling oil was "it is imperative that I survive". He believes, from the prophecy, that he is the one that will guide the world to the Dawn. Yamato isn't able to reconcile this part of the prophecy until they learn that Momonosuke is alive, at which point Yamato realizes Momonosuke plays the role Oden believed was his. Yamato is willing to die for Momonosuke not because they think Momonosuke is their son, but because Momonosuke is that important.
- Encounter with Ulti: Luffy has now freed Yamato, reinforcing their belief that they are the free man that will aid the pirates against Kaido. Yamato says "today is the day when I become Oden". Ulti is confused by this, as this is the first she's hearing about Yamato's "identity crisis".
- Meeting Momonosuke: Yamato is surprised to be entrusted with Momonosuke by Luffy; why would Luffy trust Kaido's child, who he met 5 minutes ago, with the leader of the Samurai? However, Yamato remembers that they fit the role "Oden" from the prophecy, and Luffy's trust follows as a natural consequence.
- Protecting Momonosuke: When Yamato finally catches up to Momonosuke, they say "I used your father's name earlier, but my other name is Yamato!" From here on, Yamato uses Oden's name only in the context of opposing Kaido, because they want to fulfill the prophecy. Yamato patiently explains: "Kaido is my father... But don't worry, I hate him! I told you, I'm Oden, right?" This is also when Yamato realizes that Luffy, the one that Momonosuke brought to Wano, must be the one Oden was waiting for.
- Challenging Kaido: Armed with the knowledge of Luffy's role in the prophecy, Yamato accepts the role of "Oden", or the one who helps the pirates take down Kaido. "How can I call myself Oden if I don't fight for Wano?"... Oden abandoned Wano, but "Oden" is the one who will fight for it. Again, Yamato doesn't claim to literally be Oden, but is instead using the name.