The Sweet Ghost Girl is one of the "Three Souls" or Ghost Children trapped inside a wall by the Other Mother. She was Mrs. Lovat's twin sister and would've been Wybie's great-aunt. A doll that resembles her can be seen in the beginning of the film before being converted to a doll resembling Coraline. So it's implied that she was the most recent (and final) victim for the Other Mother's grasp before Coraline. Her real name is a mystery since she doesn't remember it. She was freed from the Other World when Coraline found her eyes. The Beldam put her real eyes in the circus ball that was used for the Other Mr. Bobinsky's jumping mouse performance.
It is likely that the doll resembling Coraline is over a century old, as the Other Mother might have converted it after the Sweet Ghost Girl fell victim to her, and left it with Wybie's grandmother all that time before Wybie gave it to Coraline.