He steals the idea from Miles. Gregor figures, why should Miles be the only one who gets to leave all the Vor crap behind when he feels like it? For the good the Imperium, of course.
Illyan asks, looking, for obvious reasons, worried, "you want what? Sire."
"A name that can stand up to any scrutiny or background check," Gregor says. It shouldn't be too hard; ImpSec does it all the time for their deep-cover operatives.
Illyan comes back the next day with a dossier and all identifying documents for one Paul Lauzon. Lauzon is a man so boring that Illyan must have created the identity himself, instead of handing it off to the subordinates who usually do it and who understand that anything that seems this bland and boring and typical, can't be. He was probably concerned that any interesting detail might give Gregor ideas. Gregor takes the documents and puts them away long enough, he figures, for Illyan to stop watching the spaceports with more paranoia than usual.
Gregor submits his first article to the student newspaper at Vorbarr Sultana University four weeks later. It's rejected. The fifth one is accepted, though, and Gregor smiles for a day in sheer joy over it.
Miles, of course, figures it out in under a week. Apparently, he was reading back issues of the Hassadar Daily News one day while on bed rest and something struck him as odd in the opinion section about why more proles need to get galactic educations. Gregor supposes he should be grateful there wasn't a body count and that no one's career was ruined over it.
"But why?" Miles asks, very confused.
Gregor smiles tightly. "It's the only thing I've ever done," he says, "that I know I haven't accomplished because of what I am."