The female dragon who becomes Toothless’s companion in How to Train Your Dragon: The Hidden World is the Light Fury.
The Light Fury appears as a pale, fast-flying dragon who initially avoids Toothless and the humans of Berk. Toothless becomes fascinated by her, and their courtship forms one of the film’s major storylines. Her presence also helps Hiccup understand that Toothless has a life and future beyond his bond with one human rider.
Although her appearance and abilities resemble Toothless’s, the film identifies her as a Light Fury rather than another Night Fury. Her pale coloring provides a visual contrast with Toothless’s dark body, while her camouflage abilities help her disappear against bright surroundings.
The Light Fury is not given a personal name in the film. “Light Fury” is the species designation used by the characters and official franchise material, making it the canonical short answer.