It's because Naminé isn't a member of Organization XIII that she doesn't have the X in her name.
Though, that begs the question, who did name her? I've always gotten the feeling that she was found in Castle Oblivion already named, and the Organization just decided to use her for their own purposes.
If that's true, then who named her? Obviously not someone from the Organization.
If it's not true, then why would the Organization name her Naminé? Even if she doesn't fit in with the Organization in that she has no X because she's not a member, you'd think they would have tried to name her something close to her Somebody's name, like all of the rest.