What is the name of Bud's father?
I believe that you are asking about Bud from the book Bud, Not Buddy by Christopher Paul Curtis. Bud never finds out who is father is; therefore, the reader never learns the real name of Bud's father. The man who Bud believed to be his father, Herman E. Calloway, is actually Bud's grandfather. Most of the book focuses on Bud's search to find his father. He has very little to go on, but manages to track down Herman. Bud believes that Herman is his father.
I pointed right at Herman E. Calloway's big belly. "You know it's you...I know it's you."
Herman denies being Bud's father, but Bud does not believe him. Eventually, Herman figures out that there is some relation. Bud's mother is his long lost daughter. She ran away from Herman with the drummer in the band. That man is presumed to be Bud's father, but he is not named.