Abdiel is a biblical name used by several fictional and real people. Nevertheless, Abdiel is better known for being a Seraph in John Milton's Paradise Lost. In this novel, he is the one that denounces Satan or Lucifer for the revolt against God and abandons him to tell God about his defection. However, when he arrives, he realizes that preparations were already underway for battle. In the fight, he smites Satan, Ariel, Ramiel and Arioch, among others.
"A high-ranking angel that is devoted to God. The name carries the meaning of "slave to God," which supposedly originates from the Arabic word for "slave". Of the angels who followed Satan, Abdiel was the only one to reject the temptation to rebel against God, and instead received praise for returning to His side. Abdiel took the form after resolving to protect the order that God created and thus fell to darkness to obtain power greater than that of the angels."
—Shin Megami Tensei V lore
Abdiel is the archangel that leads the forces of Bethel, and is the angels' commander. Unlike her soldiers, she is suspicious of the concept of free will, though she respects humans and believes that God's law is ideal for them. Part of her loyalty is due to shame, as she was initially tempted to rebel against God, and in self-punishment tattooed herself with cage designs as an eternal reminder of how tempting the ways of chaos are.
Abdiel was first met right after escaping back to the real world Tokyo trying to kill the protagonist protagonist alongside several Angels on the fact that he is a Nahobino, an existence that would directly be in violation to God's law. Tao Isonokami had to lie to Abdiel to get him out of trouble's way, appealing to her faith in God and the unshakeable nature of his laws, putting the protagonist off the hook. This also boils down to her refusal to acknowledge Lucifer's words of slaying God as the truth, dragging the fight between angels and demons for years, even if their enemies have long considered their war to be won.
After the protagonist slays Arioch, Abdiel is surprised to learn of his death by the protagonist's hands and thanks them for their service, although warning them that she will still judge them as a Nahobino. During the Bethel's summit meeting with other branch representatives, Abdiel tries to convince the others of Bethel's noble cause, although her words fall on mostly deaf ears as they are more interested in the empty Throne. Their direction is greatly supported by the existence of the Nahobino among them: as such, Abdiel instantly tries to exterminate the protagonist to invoking God's laws on him and prove her point, only to be defeated and her reality shattered, left behind on the summit by everyone else, now convinced their God really is dead.
Ichiro Dazai, who she became close to (and the holder of her Knowledge), consoles her, at which point Lucifer's voice contacts them and encourages her to stand up for what she believes is right. Dazai convinces her that in order to save God's order, she must violate the letter of her own oath to not interfere with humanity, and she willingly allows herself to be corrupted to gain the capacity to do so, becoming a mutated Fallen. Freed from her restrictions, she vows to become the demonic half of a Nahobino with Dazai. The irony of the situation is not lost on her, and if the protagonist also chooses to uphold God's order, she treats him civilly and respectfully.
If the protagonist sides with another duo, Abdiel will always be the first boss towards the path to the throne.
Shin Megami Tensei IV DEMONIC GENE
Abdiel is an angel servant of Mastema, who reveals to Walter the truth of Gina's origins of a successful human made from the genes of demons, while Hiruko is the failed product of the experiment.
Abdiel as he appears in Shin Megami Tensei IV DEMONIC GENE
In Other Languages
In an interview with Masayuki Doi on Shin Megami Tensei V, on her design they had to lean heavily on original interpretations, due to there being very little reference for her in the source material. 
Her SMTV design's triangular armor is inspired by the concept of the Holy Trinity, her head and facial ornaments are reminiscent of the cross, and the design of her sword.
Additionally, the tattoos on her arms and legs represent her loyalty to God, and are visually meant to evoke prison bars. This is because they were engraved by Abdiel herself, as she was ashamed for being deceived by Lucifer and almost becoming a fallen angel.
According to Doi, Abdiel has more symbolic elements in her design, but since they might lead to potential spoilers, he would keep them to himself for the time being, before the game's release.