But this is EVA. Where they used DNA from LILITH in Rei's making.
Never stated in the series or Gainax/Khara supplemental material. Here goes what should be my last post on this subject in this thread, since I have already revisited it too many times and I feel bad for shitting up Stryp's story thread:
Info on Rei's lineage and relationships wrt. NGE canon
In NGE proper, we hear that Yui Ikari was the "primary donor" for the cloning project that became Rei. We also see an image on Yui's wedding invitation of a stylized angel which looks like Rei, and hear that Yui's naming plans for her child were Shinji if it's a boy and Rei if it's a girl. We hear that Rei had Lilith's soul put in her through a salvaging process that isn't explained.
In the "Red Cross Book" that Gainax handed out to folks who viewed EoE in theaters, it is stated that Rei was cloned "from the salvaged remains of Yui Ikari".
In the Confidential Information section of one of the Eva games (which Anno was interviewed extensively for), it is stated that Rei was "copied from Yui's flesh".
In a 1997 interview, Anno had this exchange:
Anno: Yes. [Murakami's "Ai to Gensou no Fascism"] is a story of the Oedipus Complex, where one kills one's father and violates one's mother. However, when I started [Eva], I thought the same [way]. Because it [was] a story where Shinji kills his father and steals his mother from him.
Takekuma: A mother who has become a giant (laughs).
Anno: There was this replacement by a robot, so the original mother is the robot, but then there is a mother of the same age, Rei Ayanami, by [Shinji's] side. [She is] also by the side of the real father. There is also another father there, Adam, who governs the overall course of events. An Oedipus Complex within these multiple structures; that's what I wanted to do. "Ai to Genso no Fascism." I think there are ideological elements that are the same as those in the novel. [...] The thing that most moved me was [the fact that] when the protagonist, Toji Suzuhara, attempted to kill the current Prime Minister, he felt [the Prime Minister] was very much like a father. He thinks, I will kill my father, and violate my mother, Japan. So, he goes on to destroy Japan. I really like that passage. I like that Ryu Murakami's real feelings come out there. The novel itself is extremely boring, however (laughs).
Information pertinent to other canons:
In the (separate?) Rebuild canon, I believe Fuyutsuki states outright that Rei is a clone of Yui somewhere during 3.33. This is besides the maiden name shenanigans.
In the separate SIRP canon, Rei is stated to be a cousin from Yui's side of the family. This is distinct from the NGE Episode 26 AU which SIRP is supposed to be based on, where Shinji appears to be totally unfamiliar with Rei when she is introduced.
In the separate "Angelic Days" canon, Rei is unrelated to Shinji (it's a different manga that was also inspired by the Ep 26 AU via the GoS2 game, I think - there are so many spinoffs that I find it hard to keep them straight).
Side note: I am curious which interview
@Strypgia was referring to when he said Shinji and Asuka were meant to be perfect for each other but kept apart by their trauma. All I've found re: their intended relationship at the outset is an interview with Sadomoto stating their relationship was meant to match that of Nadia and Jean in
Nadia of the Blue Water.