Elfnein's name's meaning and origin are far more intricate then those of Carol's Autoscorers. First, her name is a combination of two German words, Elf, meaning eleven, and Nein, meaning no.
Second, one must know that she represents an Arcana from the Rider-Waite tarot deck, specifically the card Justice, the eleventh card in the deck.
Carol states multiple times during the course of the third season that she does not care for the world or the people in it, and is only driven by anger and revenge, so she would have no need for justice.
As such, she would have no need for the Arcana Justice, no need for the eleventh card, and as such, no need for Elfnein.
Her name also foreshadows her role in bringing down Carol by helping S.O.N.G., leading to her defeat and delivering justice.
Elfnein is a small, fair-skinned girl with short blonde-green hair, most often seen wearing a white dress with brown stripes near the bottom. She looks nearly identical to Carol. She was first seen in a semi-revealing cloak (much to Chris' embarrassment), colored black and purple with blue inside the hood, with boots of the same color. As of now she wears small black Mary Janes and long socks. Her original body is genderless, possessing no primary or secondary sex characteristics.
After being given Carols body in GX Episode 13, she is now identical to Carol and is biologically a female, as she is capable of equipping a Faust Robe.
Elfnein's dress in GX.
Elfnein's appearance after fusing with Carol.
Elfnein's AXZ outfit, minus lab coat.
Elfnein is incredibly timid, but smart. She is curious and rarely gives up on a problem (as Maria taught her), and is incredibly reliable to the team. Elfnein also cares about the lives of others very much-even going as far as sacrificing herself for Aoi Tomosato and pleading Genjuro to chain her up when Carol was discovered to be spying on them through her eyes. She cries easily, but has grown exceptionally brave since the season premiere.
She is prone to cowardly words and actions, however she is strong at her core, and has been known to take drastic and brave actions at times.
Elfnein carries a small box containing Dvergr Dáinn's Legacy and tries to flee from Carol and Autoscorer Leiur Darāhim who keep pursuing her but then runs into Chris Yukine.
Elfnein later revealed the small box contain few pieces of Dvergr Dáinn's Legacy, the Dáinsleif sword. It is Relic with double edged and only cursed melodies can activate it. When all Symphogear user got defeated by Carol's Noise#Alca-Noise and Autoscorer, she have no choice but to proposed Project Ignite. With the help of Elfnein's alchemy, not only their Relic was repaired, but also boost their power exponentially.
Elfnein was sent together with Symphogear user to do "training" in the form of playing some beach volleyball. While they were doing that, Maria taught Elfnein how to do an underhanded serve, and said that it's okay if it's weak, as long as she's true to herself. With the sudden enemy attack of Garie Tūmān, Maria tried to use the Ignite Module, but lost control and got defeated, with Garie withdrawing. After that, Garie returns again to pick another fight with Maria. Maria was nervous about trying to use the Ignite Module again, but when Elfnein reminded her of what she had said before that is it's okay if it's weak, as long as she's true to herself. Realizing weakness can enable one to gain true strength, she managed to successfully activate it and defeated Garie.
Elfnein got injured while protecting Aoi Tomosato when HQ of S.O.N.G. got attacked by Leiur Darāhim's giant form. While in injured form, she still fight Carol in her own way by supporting Dr. Ver to rewrites the Chateau's program to stop the disintegration and recover the disintegrated parts of the world. When Carol laments her failed plans, Elfnein explains what her father really wanted was to bring harmony to the world and give the world forgiveness.
After the Magical Girl Incident, Elfnein's condition declining. After all the Symphogear user and Miku visited Elfnein, later that night, Elfnein is approached by Carol, who appears to have lost all of her memories, seeing Elfnein's declining condition and Elfnein's strong desire to stay alive, Carol decided to merge with her to become one.
While Chris and the others rush Stephan to the hospital, Maria's team go up against Prelati and Cagliostro as they launch a Noise attack on an airport. Despite running low on LiNKER, the girls manage to surpass their limits thanks to Elfnein's encouragement in promising she will do her best in finding the final key to analysing Ver's LiNKER formula to create new batch of LiNKER.
As Saint-Germain uses a new type of Alca-Noise to surround Hibiki's team in a subspace pocket that makes the Alca-Noise resistant to normal Symphogear attacks, forcing the girls to activate their Ignite Modules to hold them off. With Elfnein's idea to locate the center of the subspace pocket, however, Chris manages to use everyone's singing as a sonar to locate the Alca-Noise creating the barrier and destroy it.
Elfnein theorises that the final key to analysing Ver's LiNKER formula lies in a power that awakened in Maria's Symphogear during desperate times. To investigate this possibility, Elfnein uses a mind transfer machine, Electromicroscope Beatrice to enter Maria's memories, experiencing all the hardships while training under Nastassja. As Elfnein manages to join up with Maria's fighting spirit, they are both caught up in a strange field where they encounter Dr. Ver.
Maria and Elfnein find themselves in the depths of Maria's heart containing all of her fears and doubts. Just as she becomes swallowed up by the thoughts, she comes to understand that Nastassja cared more for her than she realized, giving Elfnein the key to finishing the LiNKER formula; love. As regenerating Alca-Noise fortress going towards Lydia, however, the fortress is stopped by the arrival of Maria's team, who are now able to fight freely thanks to Elfnein's completed LiNKER formula.
As Elfnein goes through files containing the past, she witnessed a clump of waste matter that was transmuted by Hibiki. She then proposed a Symphogear upgrade plan in order to cancel the Philosopher stone's effects. In the next day, the girls went out to search for that waste matter known as the "Fool's Stone", as named by Chris.
After the defeat of Divine Weapon Tiki, Adam Weishaupt tried to use his robotic arm to absorb the power of the Gods released from her. However, that power was transferred to Hibiki instead, transforming her into a giant cocoon. With Hibiki turned into a giant cocoon, the UN will now prepare for attack. Meanwhile, Elfnein figured out a way to turn Hibiki back to normal, which is to inject her with an Anti-LiNKER. Genjuro then called out for Miku as their "trump card" in order to bring Hibiki back.
As Adam showed his true form, a giant puppet monster. Adam easily overpowers the girls, and when he makes his finishing blow, the girls were forced to sing the Superb Song, with the help of Elfnein who used a bypass to divert some of the strain to the Dainsleif in order for them to not explode due to overload. After that, the girls transformed their Symphogears into their Last Ignite mode. With Hibiki's Gungnir transformed into a Chrysopoeia form, Hibiki finally killed Adam once and for all. In the epilogue, Elfnein informs Genjuro about Hibiki and the Curse of Balal, and that Hibiki wasn't the only one who got struck by the Shenshou Jing's light, the other person who was also struck by it was none other than Miku.
In Senki Zesshōshinai Symphogear AXZ, it is shown that Elfnein uses her free time to try and "revive" Carol by using Dr. Ver's direct feedback system to scan her memories for fragments of her memories. She calls Carol the friend she longs to see the most.
It is revealed that while Elfnein used the Electromicroscope Beatrice to examine her brains internal storage, Carol repeatedly copy-pasted the fragments of memories she was able to pick up and alchemically rebuild a stable pseudo-personality. She was able to revive her consciousness in the body she gave to Elfnein, and now currently shares a single body with her. When Vanessa about to give Elfnein one last kick, the desire to pay back the kindness and help given by the Autoscorer to Elfnein, gave her the ability to switch position with Carol, allowing Carol to battle against Noble Red.