The reasoning for the suggestion of the spelling of her name is a plot spoiler, but...
Late into the game, it's revealed that Airy has been deceiving the party from the start. From around this point, whenever you select a file that has reached that point, the subtitle changes from "FLYING FAIRY" or "WHERE THE FAIRY FLIES" to "LYING AIRY" or "AIRY LIES", depending on whether you're playing the Japanese or English versions, respectively. For reference, see the following image: i-njoy.net/image/bdff_09a.png
Given this, I believe the character tag should be aliased to read as Airy.