Going into rampant speculation mode here.
I would put it down to a combination of his hand being forced and him being caught off guard. He would have stayed off radar as long as he could, but I think he was genuinely surprised by Alphinaud's presence, and the remark about "Some small history with your order" was not something he would have intended to say if he had been thinking clearly. He soon recovers and gives them the false name.
Assuming it is Gaius, I imagine his mind changed the instant he saw the Castrum blowing up around him. He curses Lahabrea for the act - "this was not my intention" - and, I suspect once he is rehabilitated, he sets out on this course.
As former viceroy of Ala Mhigo, he would probably know how to cross his own Wall undetected. As a high ranking Legatus, he would still have contacts. Maybe he couldn't trust anyone in the XIVth, or those few with him are the only ones he could trust? Or he's picked them up on the way. He would also know imperial territory very well, and would know the good places to hide.
Last random note on this; Fordola.
Whatever is to come for her, if she lives, a reunion with Gaius is probably on the cards. Maybe she will be the one to actually "unmask" him? I know they're on opposite ends of the world at the moment, but that can change.