I guess that I have to think that the name “Lucinda” was used in the film more because of its symbolism and because it’s a name that has a bit of a period quality. It was much more common in the 19th and early 20th century and contains the root meaning of “light”.
The movie strikes me as yet another foray into masculine psychology – or the group psychology of a society run along patriarchal principles – in which the transformational figure is feminine or personifies the feminine principle. There is an entire genre of these things.
Kent