Given Aidairo's (creator) naming trend of using numerical kanji in character names, it's very plausible that Yashiro is somehow related to (or is going to be) the 8th School Mystery. Her last name "Yashiro" contains the kanji "八" (which means eight), and "尋" (which means search.) This could possibly imply that Nene is looking for truth (such as the truth behind the Mysteries of the school.)
Another interesting angle is that Hanako's real name does not contain a number. Despite being the most powerful entity/leader of mysteries,"Yugi Amane" (柚木普) has nothing to do with the number seven. The literal meaning of his given name is "normal" or "average". The word choice here could hint at the possibility that Yugi might not be the real/permanent Hanako.
The idea that there are multiple Hanakos comes from the original three pilot chapters that were published before the manga was serialized. There was a scene where Hanako mentions to a confused Nene that there had been multiple Hanakos before him that failed their jobs. There are two silhouettes that in the panel appear to be girls wearing traditional female uniforms.
While those chapters are presumably not canon anymore, it leaves the feeling that "Hanako" was designed to be a transferable position, passed down from generations of girl ghosts.
Yugi being a boy makes me guess that he's somehow an anomaly in the system. (I'm going to refer to Hanako strictly as Yugi from this point on to avoid confusion with the "Hanako" ghost position.)
Another important aspect of the story is time travel. From the recent chapters, we know that Nene has traveled back in time to the past via a dream, and successfully made contact with the young Yugi. We see Yugi using Nene's collected charms (tags) to make a wish to see her again. That wish is the key to this theory. Due to the drastic difference in time periods, there are two options presented here.
Option 1 The only way for Yugi to fulfill his wish and remain human is to naturally grow old. He would somehow meet young Nene by chance as an adult. However, Aida-sensei has subtly shown this possibility to not have happened. During the library arc, Tsuchigomori stated that the future where Yugi grows old and becomes a science teacher was rewritten. I'm assuming that as a human science teacher, human Yugi wouldn't have met Nene at all (also I'm not exactly sure about how many years Nene/Yugi are apart, so it's also possible that Yugi would die of old age before Nene is even born)
Option 2 Due to his wish, fate was deliberately rewritten so that Yugi would become "Hanako" and meet Nene as an ageless ghost. Thus, Yugi's wish made his death and his murder of Tsukasa inevitable. (He had to die, and also had to have reason to stay around as a ghost.) It's also implied by the scars on Yugi's arms in the flashback scene that he was either self-harming or abused (more likely abused). I think his family life probably wasn't very happy. Maybe I'm just reading too much into it, but the young Yugi at the festival seemed very happy/normal (absent of any scars). This gives the grim feeling that whatever abuse/misfortune Yugi suffered was caused by his wish (so that he could murder his brother, die, and become a ghost). This is all to say, if he hadn't met future Nene as a kid and made that wish, he would have grown up happy and lived a normal life.
It's ambiguous if the current Yugi as "Hanako" recognizes Nene as his mystery childhood crush from the festival, or if he remembers the festival encounter at all. I'm leaving that aspect of the theory open since it's not fully explored yet. It's possible that Yugi has forgotten the wish of meeting Nene a price/sacrifice/punishment for becoming Hanako.
Regarding Nene — it's my theory that Nene will eventually learn Yugi's full backstory and prevents him from becoming Hanako. Knowing about Yugi's tragic past, Nene might travel back in time again to stop those events from happening. (She might also learn that her encounter with Yugi is the cause of all his suffering, but that seems unlikely).
However, this would then disrupt the current timeline and interfere directly with the cycle of death. We know that Nene has to die sometime in the near future. My guess is that she sacrifices herself in place of Tsukasa and Yugi for their fated deaths, thus balancing the cycle. It also fits with the "cause and effect" theme of the theory, with Nene's time travel loop altering Yugi's future. (Other established instances of "cause and effect" include: Kou failing to befriend Mitsuba while he was alive, Sakura/Nene being forced to pay for their wishs, the effect of rumors on ghosts)
Everything comes a price. The only way to change destiny and cancel out the imbalance created by the brothers surviving into adulthood, is for Nene to die instead and become the new Hanako. The story would then come full circle with Nene as the bathroom ghost, waiting for Yugi to appear as a human in the alternate timeline. Their second meeting would also echo the first, where (an amnesiac) Yugi hears the Hanako legend and makes a wish in the girls' bathroom, summoning the ghost Nene.
