I think I remember hearing that the FFVII demo had "Aerith". Anyway, it officially should be "Aerith" since its the way they had it in Japan (It was written in roman characters, not katakana so its obvious they meant it to be spelled that way) and since FFVII was first made in Japan, and belong to a company that is Japanese, it is the official way. FFVII had many translation errors, that may be one of them, and that is why they changed it to Aerith in KH to correct that error.