Moe was not born of the Kuroki Clan originally, being the clan is rather young in itself. Rather, she was born in the Land of Grass to a family of Kemonoken, the Maki. Being of the eldest three of the family, she was focused on heavily, yet, compared to the rest, she was born physically weak and showed no talent for Taijutsu. No Beast school they went to would perform the ritual to convert her chakra to ki, saying it would be a waste of whatever she could ever potentially be to try to force someone as physically weak as she to take on their traits.
Due to her inherent weakness, Moe was something of an outcast, even amongst her own family. She always had the feeling that she was being ridiculed behind her back, and she doubted she was wrong about that a lot of the time. Despite this, she stayed with her family throughout her childhood and did what she could to be useful. It all came to a head, however, one night in the midst of a family dispute. Moe was incidentally struck and knocked back and, in the heat of the moment, ridiculed to her face about her weakness. After a while of argument, she stormed out the door. Her family figured she'd only gone for a walk, and even she figured that would be all she was doing, yet she found herself not stopping. She continued walking until she had left their home village and then their region and eventually the country as a whole.
It surprised Moe just how far she could walk with her new determination. This was suddenly less about getting away from their ridicule and more about finding her own way and eventually showing that she could be strong in her own way. From what was intended to be a short trip, she spent years on the road. She saw war and peace and even narrowly avoided being caught in the crossfire at times. Surviving on her own was not easy, but it allowed her to discover a new side of herself. It also allowed her to see sights she'd have never seen otherwise.
Through her travels, Moe grew this fascination with snakes. She noticed they were a creature that adapted to fit any environment. No matter where she went, mountain, plain, forest, swamp, or desert, there were always snakes to be found. She even picked up a hobby of cataloging different ones she had seen and drawing them in a notebook she picked up from a merchant. While related to a type of animal, this did give her something different from her family back in the Land of Grass, and it gave her an interesting perspective on her life. She became determined to be like a snake, to grow powerful and lay in wait for the opportunity to one day show the family that scorned her just how powerful she became without them.
After several years of wandering between different countries, Moe had a rather unlucky night in the Land of Wind, or at least it seemed to be at first. A group of bandits passing through came upon her campsite and decided she would be easy pickings. She'd already been roughed up a bit when a group of Kuroki who the bandits had stolen some things from while they were out of their campsite tracked them to the campsite. With authority the Kuroki quickly dispatched the bandits and recovered their belongings that had been stolen. By some stroke of luck, one of them felt sorry for Moe and decided to bring her back to their camp to have her wounds tended to.
In another case of what was supposed to initially be a short trip, Moe took a liking to the Kuroki, how they operated as well as their jutsu, and she wound up staying with the group. At first, she was only a bit of a maid, earning her keep with day to day tasks. However, after a couple years, the clan came to trust her enough that they decided to make her one of them. Casting aside the surname Maki and taking on tattoos made by the Kuroki Elders, she became Kuroki Moe. Through practice, they found that, despite her lack of physical strength, Moe had a talent for Ninjutsu and had potential to become a powerful Tattoo Manipulation wielder. She had found somewhere she fit in, a family that, while not the coddling and adoring family one might hope for, respected her and would make use of the abilities she had.
At the forming of the Hidden Villages, the Kuroki Clan surprisingly joined into Sousa's ranks and gave up their nomadic ways. Though she wasn't involved in the agreement directly, Moe figured Sousa must've had some extremely compelling offers and arguments to offer the Elders. Since they'd taken her in, she gave no argument to moving into the newly formed Sunagakure. Though she was older than most, due to her late start, she was inducted at the rank of Genin so she could start at a slower pace and build up as she built her skills.
Over the decade since the forming of the village, Moe has spent her time honing her skills in the art of Chakra Tattoo Manipulation. She proved herself thoroughly in skill on her missions and tests setup by the clan, and thus she was recently promoted to the rank of Chuunin. With her new rank, she hopes to serve the village well along with her clan… and in her mind she hopes to use the power she is gaining to one day make a strike and, not kill the family that scorned her, but prove herself to be better than them with the power she will gain.