She came into the cargo bay that they used as living quarters, and saw him shoving her few belongings into her scavenging bags.
"What are you doing?" she asked.
"You're leaving, and you're taking her with you" he replied, shortly, jerking his head towards the small girl, napping on her cot.
She was shocked. "What? Why?" He sighed and stopped packing.
"I know she's not mine" he said.
"What!? Of course she is! There has never been anyone else!" she protested.
"No. She isn't. You know how I know? Back in the First Order, I was part of the engineering group that was constructing Starkiller base. We were tunneling out the sub-surface spaces. The rock we were clearing was laced with radioactive ore. The First Order most likely knew but didn't care. I'm sterile. I can never father a child." He said, his eyes boring through her.
"No! There never was anyone else, I swear!" she assured him.
"Anyway, I'm not willing to throw away resources I work so hard for on a child that's not mine." He began packing again.
"Why now?" she asked.
"You were so happy when she was born. And she didn't require much; at first you were nursing, and then as a baby, she wasn't a burden to feed. But now? And as she grows, she will only need more and more. We are barely surviving as it is. And she can't even help provide for herself. I just can't anymore. I won't starve for her."
"No, you can't make us leave!" she cried. "Please, give me some time, I'll think of something!" she begged.
He sighed. "I doubt you will come up with anything, but I will give you two days. Then I'm leaving you and her behind."
She was devastated. There really was no way the child couldn't be his, but what he had said….it made no sense to her. She loved her daughter fiercely, had named her after a beloved great-aunt on her mother's side. There had to be a way. For the next two days, she racked her brain every moment, desperately trying to think of something to save her daughter. She herself had never been much of a scavenger. She had been starving when she met him and he had taken her in. They did work together very well as a team, but she would never make it on her own, and she could never be able support herself and her daughter alone. And the ship belonged to him. If he left, he would take their only shelter and supplies. And, like him, no one on Jakku would be willing take on another mouth to feed. She refused to even consider the idea of abandoning the girl alone in the desert. There had to be a way to give her a chance.
The solution came to her late at night. The girl and the man were sleeping peacefully on their cots, but she was restless. She sat outside, looking at the billions of stars in the clear desert night.
Plutt. The idea made her sick. Unkar Plutt at Niima Outpost was always looking for workers. And he preferred children. They could easily be bullied into working hard, and they required fewer resources. Her daughter would virtually be a slave. But she would be alive. She would learn what she needed to survive on this world. And Niima was on the other side of the planet. There was no chance she would ever have to see the daughter she was going to abandon. She sat alone in the night, sobbing over the decision she had made, but it her only choice. After she felt emptied out, she went inside and sat beside her sleeping daughter.
"I'm so sorry," she whispered. "I wish there was another way. But I know that you are strong. I know that you will be alright somehow." She gently kissed the girl's damp forehead. "I love you my darling Shimi, and I always will."
A/N:
So here is my thinking - yes, in TLJ, Ren tells Rey that her parents sold her off for drinking money. But, he got that from Rey - he told her that she had always known. I think that this was what Rey always thought about her parents, deep down inside. The thought that came to her when she angrily asked herself why they would do this. It's easier to think of them as terrible people who gave her up for terrible reasons, then to think that they loved her and still gave her up.
And the name? I saw somewhere that the helmet Rey had in TFA actually had some form of Rey on it. What better way to completely cut off your parents than to give up the name they gave you, right Ben Solo?