George's answer is spot on, but do add additional explanation in the biography. Here is an example of a note I included in a biography for one of my ancestors:
"Note regarding surname: The family surname was generally spelled "CARNES" when found in references to John's father, William. The spelling changed in the following generation. Among William's children, the name was, at their respective deaths, variously spelled "CARNES" (those who remained in Illinois), CURNES (Abel and John, who settled in central Iowa) and Curns (Reason and Phillip, who settled in Colorado)."