beyond the sea
The two boys she plays with. Sora, of the sky. Riku, of the land. The ocean is between land and sky; as Kairi is between Sora & Riku. In more ways than one. She can bring them together, and also cause rivalries between them. She's sort of the like the 'rift' which broke them apart: but also brought them back together.
As the 'ocean' she is a free spirit. She can go wherever she pleases, and her philosophy expands wide. This is similar to the sky. She can never reach high up to her goals. She is a vortex of emotions. This is similar to the land. She can be with either of them, and have some obvious similirities. She seperates them in a blink of an eye; a rivalry to restore her heart first. She brings them together, as she did when she pleaded Riku to stay for Sora to identify him. In ways, I guess she is closer to the land, Riku. During the first game, she always winds up in his clutches; as the ocean always flows over the land.
Kairi, being the 'fire to feed Sora's anger' as Saix put it, is, unfortunately, kidnapped a lot, or finds herself having bouts of courage and running away. This also relates to her name, or so I believe. She knows just about all the main characters in Kingdom Hearts: the ocean is connected to everyone. She knows more characters than Sora; she knows Namine, Roxas, and a lot of others Sora doesn't remember/never met. Her legacy is wide.
And something else I also noticed. When Sora reads Kairi's letter, the door to the light appears. And where does this door to the ligh appear? In the ocean. As if Kairi IS the door to the light; which she is, I suppose, being a Princess of Heart.
Lets look at some other meanings I have found. 'Kairi' literally translated, means estrangement/seperation, and dissociation. Seperation? Isn't that just a little too coincidental? We all know how many times she's seperated from everyone and stolen away. Dissociation, means to regard or treat as seperate, while to dissociate oneself is to break any association with anyone else. Which, is also very Kairi-ish, wouldn't you agree? Within the meanings of her name, it definately suits her.