My first thought was The Tale of Princess Kaguya, which has a girl found in a forest by a couple, and given a similar name to what you remember. However, the release date for that was 2013 and that was a cartoon.
However, there was an earlier live-action film, Princess from the Moon with the same plotline, based on "The Tale of the Bamboo Cutter", where the character is even named Kaya. Summary from Wikipedia:
One day wood cutter Taketori-no-Miyatsuko (Toshiro Mifune) discovers a baby girl while he's out in the forest visiting his daughter's grave. Not wanting to leave the infant to die and because of her resemblance to his dead daughter, he takes the child home with him- only to discover that the child grows at an extraordinarily fast rate. Incredibly beautiful, the now grown child Kaya (Yasuko Sawaguchi) attracts the attention of everyone around her, including the land's Emperor. Unwilling to accept their advances, Kaya gives the men a list of increasingly difficult tasks. By the film's end Kaya returns to outer-space by way of a space ship.