Manjiro's your basic good guy, who doesn't ever do anything bad and consistently makes what seem to be the right, moral choices. So he's actually a pretty static character. He may go through a lot, but his fundamental character doesn't really change that much; his journey is external more than internal. That said, he does add extra layers of goodness as the novel develops. Because he's just that good.
Think of young Manjiro as an innocent—he's all about wonder and awe, especially when it comes to the natural world. Here's a typical example of the way Manjiro's wandering and wondering mind works:
How does a snail move when it has no feet? he wondered. And where was the tiny creature going with such purpose? Manjiro watched it, losing himself in its slow, graceful movement. (1.2.16)
He's a guy who gets all his cool ideas from observing and respecting nature. Think of him as a natural philosopher, with an emphasis on natural. He someone who notices what's happening around him, as well as someone who likes to question things—out of curiosity, though, not out of criticism. Which is why he, on one hand, rubs his Japanese friends the wrong way. As his pal Goemon says to Manjiro, "'you ask too many questions'" (1.2.47). On the other hand, his inquisitiveness is what endears him to Captain Whitfield because, as the captain points out:
"How are you going to learn if you don't ask things? Ask all the questions you like whenever you like to whomever you like." (2.4.27)
Yeah, these two are probably going to get along.
As a result of Manjiro's natural curiosity, he's also a creative, imaginative, and even romantic, thinker. So when Goemon tells him he can't be a samurai, Manjiro asks "Why not?" (1.2.32)—he sees possibility and room for unexpected things to transpire in the world, and dares to dream beyond the opportunities directly in front of him.
And when the boys have nothing to do on the island, Manjiro "humbly suggest[s] […] that [they] are the rulers—[…] the Samurai of Bird Island" (1.2.52). He's the one who guides his friend in imaginative play, offering a better imaginary experience than the one they're actually living, so much that he goes on to say:
"And from now on shall live by Bushido. And we shall defend our honor and our island and each other against the blue-eyed barbarians." He leaped up onto a rock and swung his stick over his head. (1.2.52)
This might not sound like a big deal—boys playing at sword fighting—but Manjiro is daring to imagine something different—fishermen becoming samurai, stranded young men feeling at home on this strange island they're stranded on. Plus he's breaking from work to engage in imagination, which is just not what his other Japanese friends do.
It's this same imagination that leads to Manjiro's romantic, hopeful take on his future:
Manjiro pointed to the sky. "Look," he said. Pink light rimmed the eastern horizon and ran down the sea. "Doesn't it look like the light from another world, spilling through a slightly open door?"
"It's like how I feel about America," Manjiro said. "It's as if I see this little bit of light from an open door. It promises… I don't know what! But I want to go through that door and find out what is there." (2.11.50-52)
Whereas his friend sees just a typical sunrise, Manjiro sees a future brimming with possibilities. And the thing about this positive attitude is that it's key to his ability to achieve these possibilities. After all, if you can't first dream it, how can you ever become it? Manjiro might be different from his friends, but he's ultimately all the better for being so.
These core qualities about Manjiro don't change once he gets to America. He remains observant and hopeful, both of which we see after he loses to the bully Tom in the horse race. Afterward, when he sees Tom bloody and crying in a ditch because he's just been beaten by his dad, Manjiro shows both his ability to notice the finer details of what's going on around him, as well as the readiness with which he believes in the best. Check it out:
It was odd that Tom was so gentle with his horse, he thought, yet could be so mean to people. He supposed, too, that although everyone had thought the black and blue marks he always wore had come from fighting, they probably were given to him by his own father.
"Fall down seven times," Manjiro said, reaching out to give him a hand, "get up eight." (3.22.70-74)
Instead of relishing the moment when he sees the boy who's tormented him knocked down, Manjiro recognizes how hard it must be to be Tom, so he bends down and offers him sympathy and a helping hand.
This moment speaks to Manjiro's general ability to build connections even with his enemies, an ability rooted in his capacity to imagine a different life, which spurs him toward empathy. This is what enables Manjiro to not just survive in new situations, but to succeed: He is excellent at recognizing the humanity in other people.
Because of this, in some ways, it isn't surprising that Manjiro is awarded the ultimate—and unique—honor of becoming a samurai at the end of the book. There really isn't any other character that deserves the honor more because Manjiro knows his own fundamental nature so well. Just look at how he understands himself in the final paragraph of the last chapter:
Within him, Manjiro knew, beat a heart scoured by sand, pounded by waves, burned by sun, and polished by rain and wind. It would always be the simple heart of a fisherman, but perhaps it had also become the mighty heart of a samurai. (5.41.18)
Manjiro isn't nervous about what his fate will be—jail or samurai—and instead, in the face of uncertainty, he takes comfort in himself. We see all his core elements in these two sentences: Manjiro's calm hopefulness, his wisdom, his deep respect for nature. And, of course, ultimately he becomes a samurai. It's a happy ending for Manjiro, and it couldn't happen to a nicer guy.