Izayoi

"We don't have to name the baby before it's born, you know. If you want to wait a little while, so see what they're like, that's honestly fine with me."

Inuyasha smiled.

Kagome thought for a second. As she recalled, Inuyasha actually had more significance to his name than just 'dog' and 'forest spirit'.

"Inuyasha. Izayoi… it means 'the sixteenth night' as in the sixteenth night of the lunar cycle, right?" she tried to keep her tone from letting on what she was thinking.

"Uh… yeah, I think you're right. She was probably born just after the full moon." Inuyasha had to think about it. It is not as if his mother had ever explained her own name to him. He had seen it written, and broken into parts so he could pronounce it from reading, but he had never asked how she got it. If Inuyasha had been born a human to his mother, he would have likely received attention from tutors—bastard child or no—but born the son of a demon, his mother was the only one to take on teaching him. She had taught him as much as she could in the few years he had with her, but years of disuse of the math and writing she taught him had caused those skills to deteriorate. Inuyasha could not remember many of the kanji his mother had taught him, but he could recall the few used in their names.

"Would a name like that be good, describing when they were born?"

"Not Ichiro. That would get confusing if Miroku and I ever got to talking about our sons."

Kagome nodded.

"So, tell me, Inuyasha," she grabbed an unused skewer and made her way over to the dirt part of their hut. She gestured for her husband to follow her and began drawing with the stick into the dirt.

"Your mother's name was written like this?" She scratched out the characters into the dirt.

Inuyasha affirmed with a nod.

"And your name?" She scratched out an intentional miswriting of his name.

"What? No, gimme that," he said, snatching the stick away from his wife. "We just talked about this a second ago," he scratched his name into the dirt. "This is how you're supposed to write my name."

"Oh," Kagome said, acting surprised. By that point, Inuyasha knew something was up. Kagome took the stink back from him.

She drew a careful circle around the last character in Izayoi's name, "so, these two names," and a careful circle around the middle character in Inuyasha's name, "have the same character, here."

Inuyasha looked at the writing in the dirt. It was not news to him. When his mother was teaching him to write he had inquired about the characters in their names. He had not really understood at the time, but his mother would always quietly tell him how much his father had loved his mother, and how he made sure to carry over the character into Inuyasha's name. 'He understood, Inuyasha, that you were not just his son, but you are my son as well.' He responded by asking about his ears. 'That was the deciding factor about your name.' He knew his father must have been a clever person, though he would not learn until years later—after his mother's death, after Kikyo sealed him to the Goshinboku, after he met and fell in love with Kagome—just how clever he had been. He never asked the question often, when they moved onto new topics; the discussion of his name was forgotten.

Inuyasha's eyes drifted back to his wife's. She smiled warmly as she explained; "Izayoi is a lovely name, isn't it..? Don't you think it would be a fitting name for a little girl?"

Kagome was surprised by Inuyasha's sudden scowl. "Inuyasha?" He merely shook his head. Kagome could not tell what he was thinking, but she doubted it was good. She thought he would like the idea of naming a daughter after his mother. She thought the name was interesting as well, taking a character from Inuyasha's name for a daughter of theirs seemed like a good idea at the time. She opened her mouth to speak, but noting the slight shift in Inuyasha's expression, she kept quiet. He was still scowling, but the contemplative look gave her some hope about her idea. After nearly a minute, he rubbed his forehead and grumbled something Kagome did not quite catch.

"Inuyasha?"

He hesitated, tilting his head up to the ceiling.

"Why…would you want to name a kid after my mother?"

There was…almost a sadness in his tone.

Kagome could think of many reasons, but in that moment, she gave only one;

"I would want to name her that…with the hope she would live up to the name."

Inuyasha drew his eyes away from the ceiling quickly. He stared, wide-eyed at his wife, and absolutely amazed by her.

"From all that I've heard about her, she was a good mother, beautiful and a gentle soul—an amazing woman. I would hope our daughter would grow to be a kind and loving as she was."

Kagome grabbed his hand, lacing their fingers together. Inuyasha tried to think of something to say, but after a moment, he gave up and blushed, turning his head away. "Yeah."

...

We actually don't have a clue of what Inuyasha's mother's real name is, so I totally stole it from the third movie. I thought it was clever that they took a character from Inuyasha's name to pick out his mother's. The cleverness on the part of the writers I transposed to the cleverness of InuPapa instead. I'm well on board with the Headcanon (though off because the films aren't canon) that Inuyasha and Kagome would name their daughter Izayoi.

FYI, if you separate all three of the characters in Inuyasha's name, it doesn't make a whole lot of sense, since the middle character is one way of writing "night" and the third is basically nonsense. However, separated into two parts Inu and yasha makes "dog" and an odd Chinese word for some sort of (perhaps forest) deity-similar the the Japanese translation of "demon" we're so familiar with if you're watching the English Dubs. Which makes slightly more sense. As Takahashi explains, it means that "He is a dog, but also a forest spirit" so I take the meaning as it was meant to be by fudging the transcription of the characters as "dog" and "forest spirit" in stead of "dog" and "Chinese word for some sort of deity that may or may not reside in the forest because I'm way to lazy to actually research it"