Last I heard on this, the answer was no.
Has Square Enix given an official statement on why they will not implement a character name change service? Every other major MMORPG (even ancient ones like EverQuest and Ultima Online) offer a paid or free service to change your character's name. I have come to realize that Square Enix is unconcerned about utilizing a competitive and modern business model, but I would at least like to know why something so simple cannot be done.