Kingdom Hearts Trivia: #27
Kairi’s name was originally going to be left as “Kai,” but Nomura didn’t think it was feminine enough for her character. In order to find a way to make her name sound more feminine, Nomura went through and added each Japanese syllable to the end of her name (starting with “a”) until he found the one he liked.
Thus, Kairi’s name was born!
Source: Kingdom Hearts Ultimania