I assume that you are talking about what is said in the preface that was written by Wendell Phillips.
Phillips says that, some years before, Frederick Douglass had tried to tell him his real name. At that point, Phillips told him not to tell him this information -- not his real name, nor where he was born. Phillips says that he preferred not to know.
The reason, it seems, is that Phillips did not want to run the risk of getting Douglass's relatives in trouble. If it became known that a relative of theirs was in freedom and a famous abolitionist, they would likely have been punished in some way.