Cloud's eyes moving from the girl to the manor, he answered, "It's the Abigail Winters Manor." The answer was simple but sufficient, something expected of a man like him. Even if he was only a part of SOLDIER in his head, the attitude was instilled into him.
There was a hesitation when she asked who he was. The normal answer would have been to tell her she was a nobody, but that type of greeting didn't go over well. If she was another new, confused person put here by unknown means, then maybe he shouldn't be so cold, "I'm Cloud."