You guys are making the assumption that they didn't change the names of their parents and relatives and what not. Jake's name might of been his true name, but is there any evidence that that was true for them all? I vaguely remembering a book where the narrator said that they changed the names of the people and places, but I cannot remember which (had to leave my collection behind when I escaped my mother's place).
Jake says that his brother "Tom" is a high ranking Controller. His family consists of a father, a mother, Tom, and Jake. The Yeerks now need only figure out which of their young male Controllers has a Mom, a Dad, and a younger brother, then scoop up all such younger brothers.