In Bleach, the rank of Soul Reaper Lieutenant is one that carries immense weight. These individuals are usually surpassed in power only by the Captains. In the case of Squad 11, however, their Lieutenant was, for the longest time, a deceptively powerful little girl. Yachiru Kusajishi was her Captain Kenpachi Zaraki's constant companion until she disappeared under mysterious circumstances during the Thousand Year Blood War. Ikkaku Madarame, Squad 11's Third Seat, replaced her as Lieutenant at the Bleach's end.
Yachiru's absence at the end of the series stands out because she didn't lose her life in battle, but rather simply faded away, leaving behind her uniform and badge, in Chapter 579. Her disappearance coincided with Kenpachi's defeat of the Quincy Gremmy, but there was no good explanation for what had happened to her. Then, in Chapter 668, Yachiru seemingly reappeared to Kenpachi as he laid on the ground near death, after attempting to fight the Quincy Gerard Valkyrie. At this time, Kenpachi finally gains access to his Bankai, but most sources refer to this being not as Yachiru but as his Zanpakuto, Nozarashi. They may well, however, be one and the same.
The Case For Yachiru as Nozarashi
Yachiru's seeming reappearance is very brief, and not a lot of context is given for exactly whether it's her or not. That said, if indeed Nozarashi is a separate being, and it was imitating Yachiru, it got down her mannerisms perfectly, going so far as to call Kenpachi "Ken-chan". Kenpachi also refers to the being as Yachiru when it first appears, and questions where she had gone. Of course, the very fact that Yachiru disappeared before all this occurred lends credence to her and Nozarashi being one and the same.
Yachiru's being Nozarashi does make a bit of sense when taking into account her origins. She appeared before Kenpachi as a small child after he had used his Zanpakuto to kill a group of men, and was totally unperturbed by the gory sight in front of her. She then followed Kenpachi nearly wherever he went, and they both became Soul Reapers together. The odd relationship between a bloodthirsty warrior and a happy-go-lucky child creates a situation where they each balance each other out.
The timing of Yachiru's disappearance and seeming reappearance also plays very well into the theory that she was Nozarashi the entire time, having dispensed with the need for a separate body as Kenpachi grew more in sync with his Zanpakuto. Additionally, the phenomenon of Zanpakuto spirits manifesting in the real world alongside their respective Soul Reapers is explored extensively in the non-canonZanpakuto Rebellion. While these events don't occur in the manga, it does show that there is precedent at least somewhere in the Bleach universe for such a thing occurring.
What can be said for certain is that Kubo wants us to think that Kenpachi and Yachiru have a spiritual connection as well as a physical one, and if in fact she is Nozarashi, that would confirm it.
The Case for Nozarashi Being Separate
While at first glance the idea of Yachiru being Kenpachi's Zanpakuto seems to fit neatly into the image Kubo painted of their oddly close relationship, there are certainly a few issues with the theory. Firstly, when Nozarashi reappears in Chapter 668, she performs feats Yachiru wasn't known to be capable of, including transferring spiritual energy into Kenpachi. While this doesn't disprove the theory, it does raise questions about why Yachiru hadn't done such a thing before. Was she simply unable to?
The most convincing evidence showing that Yachiru is not Nozarashi, however, is that before her disappearance Yachiru unveiled her own, unique Zanpakuto while battling the Quincy Guenael Lee. Yachiru's Zanpakuto, Sanpo Kenju, has entirely different abilities from Nozarashi. While Nozarashi only transforms into a giant cleaver in its Shikai state, Sanpo Kenju's Shikai summons two creatures which each imitate Yachiru's attacks, one immediately before and one after. The way Yachiru and the creatures work in tandem make her attacks very difficult to dodge at short range.
If Yachiru is a Zanpakuto spirit, she is alone in having her own, separate Shikai. Isane Kotetsu, Squad 4's Lieutenant, also commented that Yachiru's Shikai is unique because her blade doesn't change at all while using it. While this could potentially illustrate that Sanpo Kenju is not a true Shikai, there simply isn't enough evidence to make such an argument with confidence.
At the end of the day, it's currently impossible to say whether Yachiru actually was Nozarashi, as there are convincing arguments both for and against this theory. Yachiru's disappearance has yet to be fully explained, and it seems even the other characters have no clue exactly what happened to her. If an answer is eventually revealed, it will likely be via Kenpachi conversing with Nozarashi at some point in the future. With Tite Kubo slowly writing a new arc, the potential for that isn't nil.