Perhaps its whatever name the child most closely ties to their identity. I beleive Harry mentions this when discussing summoning with true names in the early books- Demons names dont change because they have no sense of self but the subtle intonation on the way a mortal says their own name can change as who they are does.
As a further example Harry wrests control of Bob in the final scenes of Dead Beat by reminding him that he named him. Im sure that as a spirit bob had a true name before this- perhaps it was used in the binding that keeps him inside the skull. Im sure that as a child