(For the record, I don't own x-men sorry, Logan)
He would never call her 'Rogue'. 'Rouge' was a front, a mask, to the beautiful woman only he had the privilege to see. 'Rogue' was a loner, and he would never allow her to be lonely.
He would never call her 'Marie' unless alone. 'Marie' was a sacred word, a prayer, only to be uttered by the worthy. True, he did not count himself as worthy, but he wouldn't allow any other to speak her name – it would be blasphemy.
He would never call her 'kid' in the face of others; it would only demean and humiliate her. And he would rather cut off his own limbs before hurting her in such a way. He called her 'kid' in her presence to keep them both safe – keeping her true identity a secret, and keeping himself in control of his thoughts and actions.
He only referred to her as 'she' or 'the girl', keeping her safe in his heart by never saying her name. And he had promised to keep her safe.