The Nameless Star is the spirit of a mysterious girl lingering in The Final World. While her identity is not specified, she is a form of another character who has previously appeared in the series.
Before Kingdom Hearts III
The Nameless Star was a friend of Yozora and inhabitant of Quadratum, considering it to be the biggest city she knew of. At some point, someone took away everything about her and her spirit ended up in The Final World.
Kingdom Hearts III
The Nameless Star appears while Sora collects the first pieces of his body, alongside the other stars that are still tethered thanks to a bond. She tells Sora that someone took away her name and everything about her, and that she is waiting for a particular person to come and find her. However, the person she is waiting for has been transformed by having their heart replaced with someone else's and no longer remembers her, even though he would miss her if he could. After encouraging the star not to give up hope, Sora offers to help reconnect the pair, and the star whispers the person's name to him.
Kingdom Hearts III Re Mind
When Sora meets Yozora, the protagonist of the video game Verum Rex, he is at first confused about how Yozora can be real. However, he quickly recalls the Nameless Star, saying "that girl" told him about Yozora, so he must be a real person after all.
Kingdom Hearts Melody of Memory
The Nameless Star is revealed by the Fairy Godmother to be one of the three people needed to find Sora, alongside Riku and Kairi. She reveals that she is from Quadratum, a world from "the other side", but the Fairy Godmother explains that she cannot reclaim her physical form in her homeworld because her heart would be stolen. Upon hearing that Sora is in trouble, the Nameless Star offers her assistance, and Riku uses the power of waking on her to open a portal to Quadratum.
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