Its significance

fter Naoto is rescued by Fuyumine, he asks her whether or not she is able to recall her name. Unfortunately, due to the trauma from the attack that night, she fails to remember anything of her past. At last, Fuyumine gives her a name—one that she immediately despises.

Fuyumine: Naoto. We'll call you that for now. It belonged to someone else... but you can use it until you remember.
Naoto: Now he controlled even my name. It made me feel sick.
  • Murato Fuyumine & Naoto Fuyumine
    Chapter 3: "Blade Maiden [Part 1]"
    Dogs: Stray dogs howling in the dark
Naoto's full name in Japanese is written as so:
冬峰 直刀
In English, "Naoto" (直刀) means "straight blade." As a note at the end of Dogs: Stray dogs howling in the dark mentions, "straight" can also mean "pure" or "just." The name reflects Naoto's straightforward and honest character. Despite living her life in pursuit of vengeance, thus far, she has never been disingenuous about her motives. Furthermore, she is—generally—opposed to killing or harming others without reason, making her both merciful and honorable.

Alternatively, the name also references her primary choice of weapons: knives and swords—namely her katana.

ears later, Naoto learns that her name is the same as the one who killed her parents. Aside from loathing Fuyumine at the time, this fact may also be a reason why she feels "sick" when Fuyumine decides to call her "Naoto."

"You're my spare."
When she finally meets the killer—the "other Naoto"—that person seems to have claimed a new name for herself: Campanella Frühling. What's interesting to note is that Frühling's new name holds no resemblance to her former one. A combination of Italian and German, the name is of a different origin than "Naoto" (which is Japanese), and also holds a different meaning.

So why did she change it?

Later in the series, Frühling reveals to Naoto that Naoto is her spare. In other words, Naoto is Frühling's clone. Perhaps, knowing that another "Naoto" exists, Frühling sought to change her identity in order to regain her individuality. To eradicate all ties to her clone, she claimed a new name, one vastly different from her old one.

rühling's decision is significant because while it allows Frühling herself to claim an identity, it also allows Naoto a right to her own as well. Magato, who knows both Naoto and Frühling well, compares and contrasts the two every now and then, illustrating how different they are from each other.

When Einstürzen takes control of her, Heine is forced to fight Naoto. Aside, Magato watches and comments that Naoto, in all her mindless bloodlust, is no different from Frühling.

That won't do, Naoto. It's fine if you're not perfectly righteous and proper all the time. But when you're like this, you're no different from [Frühling]. And you're not her, you don't want to be like her, do you, Naoto?
  • Magato Fuyumine
    Chapter 71: "Heine & Naoto I"
    Dogs: Bullets & Carnage
Similarly, Magato uses the name "Naoto" to remind Naoto of the kind of person she is.
Magato: Listen, Naoto. That hag will sure as hell try to slither her way into the creaks of your heart. So don't forget the name he gave you—'Naoto,' 'a straight blade.' You're the most interesting when you're being straightforward and honest by not being straightforward and honest, you see. That's why I wanna cut into you so bad.
Naoto: Then... that woman, Frühling, cast away her name because she forgot that?
Magato: Yeah. I'll tell you her little story.
  • Magato Fuyumine & Naoto Fuyumine
    Chapter 78: "Outcast & Miscast I"
    Dogs: Bullets & Carnage
Frankly, his wording (or the translation of it) is complex—not to mention a bit loquacious. Hopefully his words will bear more meaning in the future. For now, however, it is clear that Frühling did abandon a part of herself when she abandoned the name "Naoto."

To avoid the same fate as Frühling and, perhaps, to prevent Einstürzen from controlling her once again, Naoto must remember who she is. She must remember that, although her name once belonged to another, it is hers now. The name "Naoto" is her identity and it is hers to own and be true to.