Alidar Jarok wrote:
She'd presumably listed her legal guardian in the school records as her grandfather Doctor Foreman (I wonder what first name she used for him)
Probably John if the later "John Smith" is any indication.
Except the use of that name wasn't the Doctor's idea, at least not as originally presented. The first use of the John Smith alias in canon was by Jamie in "The Wheel in Space," without the Doctor's knowledge. The Doctor then used the alias again in "The War Games" and subsequently when he was exiled to Earth at the start of his third incarnation. (Jamie's independent coinage was repeated in the McGann movie when Chang Lee gave the wounded Doctor's name as John Smith when admitting him to the hospital.)
Although more recent works have complicated things. "The Vampires of Venice" showed that the Doctor's library card featured Hartnell's face and the name "Dr. J. Smith." Some tie-ins have indicated that the First Doctor used the alias when renting the Foreman scrapyard and picked it up from Susan's favorite rock group, John Smith and the Common Men (to whom Susan was listening in "An Unearthly Child"). So you could be right in light of later retcons.