In addition to being an obese jester ghost who likes to tease people or scare them, Hazel suffers from a multiple personality disorder. For the moment, what we do know is that Hazel has three personality who notice this by changing the color of her hat.
When she is pink, it's the Hazel we know who likes to tease people and likes to joke. A real jester.
When she is purple, Hazel looks depressed, sad, bored as if the pleasure of life is gone. she becomes a kind of Gothic.
When it is red, it would be better for you to flee! She becomes a real psycopath who wants to kill people and she is devilish.
Imagine the father in the film shining, but in ghost! Brrrrr ....
We do not know how she changes her personality drastically, but we know that the color of her hat changes.