Kenpachi, her Ken-chan, her role model of questionable morals, may not have had a name, but it's not like he ever conformed to any stereotypes. He broke all the rules by beating into the bloody ground anyone who tried to tell him what the rules even are. Then he effectively smashed the bad-boy stereotype he was assigned by carrying around a pink-haired baby girl on his shoulder. Finally, Ikkaku and Yumi caught up to them, and Kenpachi would have lost all respect anyone had for him except that all four of them, yes, including that cute girl, and the pink haired toddler, could probably kick your ass in under 20 seconds flat.
There's no way Ikkaku could perform that dance of his in public unless his self esteem was astronomically high. It obviously is, as Kenpachi can attest.
Speaking of abnormalities in self-esteem, there's Asekagawa. Yumi is always himself, all the time, and whether that's a good thing or a bad thing depends on whether you ask him or someone else. He has never, and probably will never, feel the desire to not speak his mind. Tact isn't a strong point, but Yumichika is always honest.
So, no, Yachiru will never be "normal". No, she won't ever go to the Academy, either. In her own words, she "doesn't need any of that pansy-ass kidou stuff when I'm in 11th!" (at which point Kenpachi congratulated her, Ikkaku dragged her off his head, and Yumichika told her to watch her language). Oh, and no, she'll never wear dresses and play with dolls. She tried that once, with Byakuya. It was boring. She couldn't play horsie or hide and go seek with Hollows, and while Yumi said she looked pretty, everyone agreed it was disconcerting.
"Do you like that... er... thing, Yachiru?" Kenpachi had asked.
"No," she frowned, "not really. It's pretty and pink, but I can't draw my sword".
Besides, anyway, Yachiru would take swords and Shinigami robes over dresses and dolls any day. Because while it might be curious to play in Byakuya's world for a day, she's in 11th.
And that means she's a fighter, down to her core. It means she has a family to protect her to their deaths. It means she will and can do the same. And that means they'll help her discover who she is, and they'll let her grow but won't let her wilt. The 11th division has no noble words, but they have a monopoly on all the sincerity and truth in the world. They will show Yachiru. And since she is just as strong as they are, she'll show them too.
