Something obviously gets transfered over, at least the alien component that Gendo actually needs, but they have ostensibly different personalities.
I think it was explicitly stated in some staff interviews that they backup her memories during the tube sessions, but that's a bit like pasted on-data.
Rei III ostensibly knows who Shinji is when she first encounters him, but she doesn't remember what happened since the last backup session, and she barely reacts to him. She only knows it, but she can't quite feel it. There's an echo of sorts, but is that really her own? At first, it stops her from crushing the glasses. But a while latter, she does crush them.
He came to check on her - the previous one always reacted strongly to such occurences.
And there are these lines from ep 25:
ReiIII: How can all of you possibly be me?
ReII: It's simply that the other call us 'Ayanami Rei.'
ReiI: We're all things that are called that.
ReiI: "You're afraid that you will dissapear from the minds of others if another exists" - there were images of the clones shown, but also allusions to Lillith made.
Basically, no one will notice she's gone, or she as a person, Rei the schoolgirl will be forgotten, because "That's really Yui" or "That's really Lillith" and she was afraid of that, with the next clone going,
"Wut, no, actually, I dun feel any fear, let's march back to Lillith. Damn Gendo for creating me in the first place."
Or the way the famous line is worded: "If I die, I can be replaced" not, "This can't kill me anyway" or "This will only destroy my body, anyway."
In a way, that scene from ep 25 was an examination of the aspects that make a person a person. There's nature (Represented by Rei I - Yui, Lillith, etc, whatever she's crafted from, and in a meta context, genetics in general), nurture (represented by Rei II - connections with ppl, most notably the Ikaris.) and the favorite of any existentialist, a person's own decisions and interpretations, represented by Rei III.
The EoTv!One seems to ultimately stay conflicted and yield to Gendo's wish, the EoE!one seems to reach some middle ground - She goes merge with Lillith, but part of her motivation is also to check on Shinji since he's apparently screaming his lungs out for some reason, and let him decide stuff.
I think Hayashibara even subtly differentiates them in the conversation, with Rei II having the usual "quiet victorian heroine"-voice and Rei III a bit more womanly, bit like Glados without morality core, but to a less comical extent. Or maybe that's just me.
But there are differences in personality - Rei III was practically always glaring whenever her expression wasn't blank, she reacted to Kaworu with mostly suspicion and she was the type to have this silently simmering resentment, she didn't turn on Gendo until the very end even though she practically hated him from day one - whenever someone got ReiII pissed off, which didn't happen often, they found out immediately afterwards because she immediately made sure to communicate to Shinji (ep 5) and Asuka (ep 16) that she begs to differ, and she didn't seem to keep any grudges, not even against Asuka or freakin' Armisael.
ReiIII resented her existence, but ReiII just thought it weasn't that vbaluable, but she liked it whenever someone did treat her as valuable, and by ep 23, she clearly told Armisael not to absorb her. Ep 25 sorta implies that she was secretly afraid of dissapearing.
And there's the entire Gendo thing - That wasn't just blind obedience, that was genuine loyalty, she wouldn't have him insulted and silently smiled to herself when thinking about him.
Yeah, Gendo may not have earned that loyalty in an entirely fair way, given the circumstances, I don't think you should be willing to die for someone who wouldn't die for you, and Gendo certainly wouldn't die for real, but that doesn't change that Rei was genuinely loyal in the way of an emotional bond.
The plan ultimately comes first, yeah, but that's the same with Gendo's biological child, and that he cares for her less than he cares for the plan does not mean he doesn't care for her at all. They do have some sort of silent understanding between them, we see them smile at each other (ep 5 and like every tube scene) they have lunch together, they discuss school.
Sure, the reason he got attached to her to begin with is that she reminds him of his wife whom she misses, he may have projected some of the feelings for his real child whom he wouldn't face, but "Rei" is what he would have named his daughter. There is a certain distance between them that you wouldn't expect between a normal father and daughter, but he wouldn't let an actual biological daughter any closer, either, that's simply all the proximity he's capable of. Yeah, he's not exactly the world's best parent by far, but he has shown on several occassion that she's no less important to him than his actual son.
There was always a certain silent understanding between them.
The most prevalent theory is that of a gradual loyalty shift, but I don't think that's what we see here. Yeah, there were indications of the distance involved but by ep 22, she'd still die for him, and there's that last flash she saw of him...
It's more a matter of, "One clone liked him, the next didn't." hence that scene in 22 where she grabs herself the glasses.
He should have invested in her more, perhaps, but he probably thought he didn't need to because he likes to think he can raise the dead.
Rebuild, including Q SPOILER: Show
Rebuild as a whole, including Q, seems to strongly push the "different people" interpretation, I think one of the staff interviews, I think it was Ogata's, had her say something like "he thought he saved her, but it was a completely different person" or stuff.
You could argue that the situation is not entirely the same since some component of Rei II is preserved in EVA 01 and didn't get transfered into ReiQ, but there's also the thematic focus there, both on Shinji saying "his" Rei is irreplaceable to him, and the scene where ReiQ converses with Asuka.
"What would Ayanami Rei do if she were here?"
"Who cares, do what YOU want!"
The interesting thing is that ReiQ is even distinct from classic!ReiIII. Yet another different way to react to the same situation.
It's also an interesting continuation from that line in ep 25 - For once, someone is NOT calling the next Ayanami Rei, cue mayor effect.
You could argue that the situation is not entirely the same since some component of Rei II is preserved in EVA 01 and didn't get transfered into ReiQ, but there's also the thematic focus there, both on Shinji saying "his" Rei is irreplaceable to him, and the scene where ReiQ converses with Asuka.
"What would Ayanami Rei do if she were here?"
"Who cares, do what YOU want!"
The interesting thing is that ReiQ is even distinct from classic!ReiIII. Yet another different way to react to the same situation.
It's also an interesting continuation from that line in ep 25 - For once, someone is NOT calling the next Ayanami Rei, cue mayor effect.
As for the room, it's not really that difficult - most people prefer surroundings similar to those they were familiar with when they grew up.
If you grow up in the mountains, you'll like mountains, if you grew up by the seal, you'll get all nostalgic at the sight of boats.
Rei grew up in a lab, so she prefers to live in places that look like labs.
