The Doctor is not programmed to be self aware. To guarantee his continued indentured servitude they have to make sure that the Doctor is self unaware and that he gets off on his unawaredness and has no desire what so ever to change that status.
If they tell him to take a bullet out of Harry Kim's shoulder after a cocked up away mission and he says "No." Do you really think that they'll let Harry die because the Doctor wants to change his name to the Princess?
Data on the other hand was created to be alive, self aware and thinking. Treat him like a slave, forget to say please, and he's going to knock you your ass, or at least the constipated passive aggressive mid 24th century equivalency.
All that being said, the Doctor could "accidentally" become self aware, but he's not going to become "accidentally" self aware, when he's specifically programmed not to be come self aware after only a month in deep space without perhaps something weird happening.