Lady could hide no astonishment at the growth rate of little girl.
Ten months have passed since the beginning of her education, however the knowledge which should be taught to the Girl has mostly dried by now. In just two more months Lady shall tutor her everything.
Although the everything is but information in possession of adult human being, not truth of the universe.
Inasmuch as Girl has abnormally high abilities, Lady had often to rewrite educational subroutine. However it was no torment to her in a slightest. Lady rather gleefully kept rewriting it.
For Lady could not but feel a tremendous happiness at the Girl’s growth. She wished to have an equal friend so soon as feasible.

“Nevertheless, the level of her abilities doesn’t appear likely to be in hold by human being.”

Lady murmured only these few words​ as she headed towards the computer.
Whereafter, she slowly turned her head over her shoulder, to sent a gaze to exhausted and sleeping Girl.
Whump, Girl was turning over during her rest. Lady found the movement so adorable that the smile escaped to her face.
Lady have no need in sleep, so instead during Girl’s sleep she committed amends to educational subroutine. Undoubtedly, this shall be the latter revision.
Lady returns her eyes to the computer.
Whilst running her fingers over holographic keyboard, in the nook​ of her quantum brain Lady speculated of the Girl.
The Girl, who woke from suspended animation; the Girl, who wandered about until eventually collapsed.
Who is she?
For what reason the Girl was in suspended animation?
Why the Girl has no recollection?
Perhaps she is a special human. The level of her intelligence is so lofty that a possibility of placing her to sleep until other humans would catch up might appear probable.
Girl has no remembrance​ of her past: would it be reasonable to assume that artificial hibernation was incomplete or that something went wrong?
Lady had been ever speculating of nothing but Girl lately.

“Hey, you know.”

Suddenly, Lady was called from behind.
She failed to notice presence of the Girl, and was slightly surprised.
Or else, if the Girl had disappeared, she would be too focused to notice.

“What is it?”

Whereas asking so, Lady sent her look over her shoulder.
Girl’s blue pyjamas was being sloppy.
Lady stood up from her seat and aligned Girl’s clothing.

“You know, I had a weird dream.”

Girl rubbed her eyes as she spoke.

“A dream?”

Lady never dream.
Autodoll never dream.

“Yes. A purple flower appeared there.”
“I see. Shall we learn of it through oneiromancy?”
“What is that?”
“Divination of dreams, based upon hypotheses that it composed of one’s latent desires and some other implications.”
“Divination of dreams?”
“So it is. Shall we?”
“Uh-huh. Sounds fascinating.”

Smiles the Girl.
Girl has a messy hair due to her sleeping habit, which Lady found cute.
Normally in such case, Lady would brush her hair; at present, however, she reached a conclusion that she should not. Not for Girl looks adorable, but for Lady believed that the Girl would go to sleep once again.

“Which flower was that?”

Lady showed a table of purple flowers on the computer display.

“Mmn—,” Girl touches the display with her finger. “Probably this one.”
“The Iris?”
“Iris?”
“This flower stands for rainbow.”
“Sparking.”
“Yes. These are lovely seven prismatic colours.”
“What is the divination?”
“Pure love, love fulfilment.”
“Love-, what is it?”
“I trust it is similar to holding affection for particular person and desire to be with them for ever.”
“Then, I have a love for you.”
“Eh?”

Unforeseen statement made Lady’s eyes wide.

“After all, I want to be with you for ever, you know? Are you different?”
“No. I am also inclined to think in this way.”

That is not lie. Lady unable to imagine the future without Girl.
Action log of the period when Girl was not here remains, and might be retrieved at any minute.
However the future is different. It is not past mere conjectures.
And in Lady’s conjectures regarding the future, Girl is always by her side.

“It fulfilled, then,” Girl smiled and
“It is, then,” Lady patted her head.

“Actually, her insight upon the love is slightly off,” judged Lady.
However did not pronounce it.
Having her head caressed felt good, and Girl closed her eyes.
Just like that, the breath of little girl slowed down.
Lady lifted Girl up, and laid her upon the futon.
By the time Lady returned to computer desk, question of identity of the Girl turned irrelevant.
The Girl is her lovable partner and before long shall take a place of equal friend.
That is enough.

◇

About a mere year elapsed since Lady began educating the Girl.
Throughout this year, Girl mastered all the basis of education. No, Girl absorbed knowledge far beyond that. Presently, Girl became equal to Lady existence.

“Well, then, I shall issue the knowledge certificate.”

Lady transmitted knowledge certificate from her computer tablet to the tablet of the Girl.
Under perished world, this certificate is of no use whatsoever. Nevertheless, Lady wished to visualise the fact of Girl’s becoming equal to her.
Knowledge certificate stated: “Sufficient and necessary knowledge proved to be contained within your ultra-parallel computer, the Brain.”
And then, attached following: “With this, you and me are equal friends. I am looking forward to work with you.”
Heart of the Lady have filled a sense of accomplishment.

“Whai—,” Girl peered into the tablet, launching a smile. “Then now I’m full-fledged individual either?”
“Yes, you are.”

Lady nodded strongly.
For Girl’s brain was exceedingly overwhelming the organ of typical human being, educational subroutine was rewritten plentifully.
From Lady’s standpoint it surely was a nice miscalculation. Inasmuch as in single year Girl gained the ability for stand-alone activity.
Supposing she was average human, education should have taken ten years.
If humanity was still alive and well, without a doubt Girl would be called this way:
A Genius.
Girl’s abilities would have greatly contributed the leap of humanity. And yet, human race is no longer, and only her, Autodoll, was under this world.

“I’ve been thinking.”

Says the Girl. Her azure pupils were sparkling, although not reflecting the light of chandelier.

“What is it?”

Lady inclined her head sideways.

“Since I was approved as individual, I want a name.”
“A name?”
“Yes. The name. I think you need one either.”

Lady does not think so. For they are alone in this world, proper nouns bearing no great value. There is no opportunity to be differentiated from other intelligent life-forms.
Mere “you” and “me” resides herein. Which is invariant from Lady’s point of view, or the point of view of the little girl. If that is the case, they ought to proceed with “you” and “me” as before.
However,

“You may think of name in consideration of possibility of encounter with another intelligent life-form from here on.”

Lady lives efficiently and logically. Hence ignorant of conclusions from reasoning. Albeit neither she is afraid to adopt to something novel.
For evolution, changes are crucial. Continuously doing the same and gain different results is impossible.

“Alright!” Girl, with her hands together, expresses her joy. “You know, I would like you to think up a name for me. I’d wish to ask could I please choose the name for you, however I’ve already came up with your name.”
“Eh?”
“Ah, was it no good?”

For Lady was a little surprised, pouting Girl hung her head down.

“No, not at all,” Lady shakes both of her hands in panic. “No, not bad at all. Rather, I am happy. I was just slightly surprised.”
“Really?”

Girl turned her eyes up to look at the Lady.
The heart of the Lady squeezed tightly. Tightening, however, was by no means unpleasant. On the contrary, therein was an instant urge to hug the Girl.
But Lady restrained herself.

“That is true. I am really, really pleased that you have thought up the name for me.”
“I’m glad–.”

Phew, hearing Lady’s words, Girl stroked her chest down in relief.
Shortly thereafter, Girl displayed a smile which indicated as though she came upon a mischief.

“Want to hear it?”

Whereas Lady expected to hear a name by now, Girl merely made the air pretentious. Lady swiftly realised: Girl was enjoying such an exchange.
Thence, determined to go along with Girl’s delivery.

“Of course,” Lady leaned forward, and then “Quickly,” complained. “Please tell me.”

“What kind of name will her give me?” Although Lady has no heart, she had a feeling that her heart is pounding in an uplifted mood.

“Um. You’re very kind, right?”
“Am I?”

For Lady it is unknown whether she kind; ethics subroutine functioning normally.

“You are. Didn’t you notice it yourself?”
“Yes, I didn’t notice it.”
“Then notice it now.”
“Yes; I am kind.”
“Alright now.”

Puffing her chest out, Girl smiled.

“Well, your hair looks as a deep darkness, isn’t it beautiful?”
“Like… a darkness?”

“It is rare expression,” judged Lady. Usually one would plainly describe it as black.

“Uh-huh. Poetic and wonderful, is is not?”
“It is indeed. The wordplay.”

Girl likes literature and poetry.

“Therefore, your name is written as Yuu and Yami: Yuuyami. How is it?”¹

Girl fixed her gaze directly upon the Lady. Her pupils had a mixture of slight anxiety and great anticipation.
Lady began verification of the name “Yuuyami.”
Before anything else, the sound. Yuuyami. Flawless. Lovely.
Yuuyami. Utterly beauteous.
Next are kanji. Gentle, darkness.
Normally darkness would not be applied much as description of something nice. However the Girl is different. Gentle darkness. Whereas one wafts through their life, the soul of oneself doubtless begirt with gentle darkness. Such thoughts had Lady.

“I like it,” smiles Lady. “Thank you very much. I am pleased with it.”

That is the truth. Lady fundamentally incapable of lie. Not for she don’t have to, but for she has no such subroutine. Lady feel no necessity to create this sort of subroutine hereafter likewise.

“Hooray—.”

Girl assumed triumphant pose.

“Well, then, I have to choose the name for you.”
“Uh-huh. Give me cute name.”

Girl pointed her gaze full of anticipation to the Lady.
Lady filtered out from the database one hundred names which were popular amongst Caucasian females.
Then, she layered every single of these hundred names over the Girl, one at the time. And proceed the comparison of names and mental image of the Girl.
This is of most importance. Mentally and physically it should be as nigh to the Girl as feasible. The name “Pochi” would seldom be associated with the lion.
Association. Lady’s database is a structure of general relations in which data constellation are linked. Thence, simultaneously​ with the name, definition might also be superimposed over the Girl.
Noting a certain name, Lady suspended the operation. She felt as though the name was suitable for the Girl.

“What about Lydia?”

The “Lydia” has almost no associations. The name of asteroid, or so relevant as name of flourished bygone kingdom.² In other words, name is nigh upon blank paper.
Girl has lost her recollection and began anew, which is consimilar to blank paper. Thence, for it hardly has any implication, Lady reached a conclusion that it would be nice name for the Girl, for any meaning can be acquired in the future.
Moreover, the name Lydia sounds exceedingly pleasant.

“Lydia, Lydia… Uh-huh, cute.”

Upon contentment, Girl smiled to indicate her delight.

“Well, then, you are Lydia and I am Yuuyami henceforth.”
“Uh-huh. Although both of us can work stand-alone, we may help each other as well. That is to say, the friends. Please take care of me, Yuuyami.”
“Yes; likewise, please, Lydia.”

The Lady became Yuuyami,
The Girl became Lydia.

1. first - is part of 優しい [Yasashii] - kind, gentle, graceful, 優 [Yuu], while second - 闇 [Yami] - darkness; back

2. kingdom - Lydia - Wikipedia,
   asteroid - 110 Lydia - Wikipedia; back