Also an "I myself am new to Evangleion Fandom" warning.
Neon Genesis Evangelion, or as I like to affectionately call it "The Anime that has the Staypuff Marshmallowman nailed to a Giant Cross", is an Anime known for it's use of Judeo-Christian imagery, not in a strictly Biblical sense but in a sense filtered by Kabbalah, Gnosticism, Jungian psychology, and general Anime weirdness. And endless debates on if that imagery means anything, I think it does, but I think the meanings are layered.
Rarely is the subject of Shintoism, the native "religion" of Japan possibly being an influence brought up. None of the names come from Shintoism, but we in the West often explore Christian themes in fiction that replaces all the familiar names with more exotic sounding ones, from Tolkien to Lewis. But even also sometimes in more contemporary settings, Shakespeare had to get around the Law itself not allowing him to depict The Bible directly.
Maybe I'm able to notice this because I had already noticed just from studying the use of Mythology in Final Fantasy games how easy it can be to construct parallels between Shinto cosmology and Gnosticism. Like comparing the Hitorigami and/or the "Seven Divine Generations" to the Gnostic Aeons.
The gist comes down to suggesting that the being SEELE calls "Lilith" is really Izanami and the being called "Adam" is really Izanagi. For starters independent of bringing NGE into it those two can be viewed as the Adam and Eve figures of Shintoism. Their names essentially mean Male and Female, and they are essentially the ancestors of everyone, human and Kami alike. In a Gnostic or Kabbalistic analogy they'd be Sophia or Lilith and Adam Kadman or the Cosmic Man. Even the issue of Izanami speaking first in the Mating Ritual could be viewed as paralleling Lilith's desire to be on top.
Izanami is currently supposed to be trapped in the Underworld unable to leave, not unlike Persephone or Eurydice from Greek Mythology. In Evangelion "Lilith" (If you're reading this even though you're not familiar with NGE, Lilith is the Staypuff Marshmellowman I refereed to above, though it was originally misidentified as Adam) is being held by NERV literally underground. If I've followed the geography correctly, NERV headquarters is a huge Pyramid built beneath New Tokyo-3, and where Lilith is being held is in a basement deep beneath that.
Also Izanami and Izanagi had a special Spear linked to them, called the Amenonuhoko. Which could have something to do with the Spear in NGE which is refereed to as the Spear of Longinus.
Also there are two characters in NGE that are effectively Human Avatars of the beings known as Lilith and Adam. Ayanami Rei is Lilith and Nagisa Kaworu is Adam. Who's names, have a plausible phonetic connection to Izanami and Izanagi.
Maybe none of that means anything. But it's interesting to think about.
As a little humorous bonus, here is a Meme I made.