Lord Justice Pitchford and Mr Justice Simon ruled the anonymity order must be discharged.
The judge said that the course used by David McGreavy's legal advisers when applying for anonymity was "wrong".
The ruling was a victory for the Justice Secretary and national newspaper publishers who all worked together last month, after the Press Association alerted them, to say that the order was legally flawed and was wrong to stop the public from knowing all the facts in the case.
Counsel Guy Vassall-Adams had told the judges that even "the nature of the victims" could not be revealed.
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Sunshine and showers tomorrow. Breezy and feeling fresher.
Clear and mainly dry overnight. Heavy showers developing during Thursday.
Her family thought that she was staying with friends but she has not returned home.