He turned on his heels slowly and considered what name to give her. There was the innate fear that if he told her who he really was right that moment that she'd definitely flee. Loki was no fool, he was well aware of his reputation and women that appreciated that sort of reputation generally knew who he was. But she didn't know who he was. He, a rather prominent figure, he liked to think, in Asgard and she didn't know who he was. He, Loki, Odin's blood brother. Did the woman live in a cave?
But still, Loki was intrigued, so he would try to avoid scaring her away. So after a moment, he answered her as truthfully as possible without giving his actual name away, “Someone you probably don't want to be seen with. Who are you, who I've never seen around Asgard?” It was a fair enough question, given he'd spotted her in a state of undress, in public of all places and then had the audacity to act surprised that someone was around.
“But more importantly, what are you doing?” Of that he was genuinely curious as well. Nothing could help that, unfortunately. He was a curious individual and it frequently got him into trouble. He was also good a lying and getting others out of jams, much to his own suffering later, but that wasn't important at the moment.