I think he is the first incarnation of the Doctor, pre-Hartnell.
I think he must have done something so bad, that
made him regenerate and then make a promise to redeem himself and call himself The Doctor now to help others.
So from Hartnell he steals the TARDIS, and runs away to explore and help people and redeem himself for whatever he had done. And that is what drives him.
Watch it again, that doesn't work because 11 makes it clear that the Hurt version breaks the promise that was made when he took the name 'The Doctor' not that he takes it after Hurt breaks a promise.