And if that is the case, then the question would probably be "Well why wouldn't Loki just be Loki?" (if you still wanted an excuse for Lady!Loki :D) So maybe he wouldn't want people to know he was Loki~? I think like Li Hua wouldn't be widely known to the public as a baddie and Mystique can just be anyone and of course Tony or Tony/Justin would be in the public's good graces. So to keep their not-bad-guy facade they would take measures to not appear to be widely-known bad guys? Idk, just throwing out ideas.