In "Bud, Not Buddy", did Bud find his father and what was his name?

Bud does not find his father. The man he had believed to be his father, Herman E. Calloway, turns out, in fact, to be his grandfather.

When Herman finds out that Bud's mother was named Angela Janet Caldwell, he is inconsolable. Angela Janet was his daughter, whom he had loved very, very much. Herman, however, always had very high expectations of himself and everyone around him, and he was especially hard on his daughter, because he knew that "this is a hard world, especially for a Negro woman...she's got to be ready". Herman was determined that Angela Janet "was going to be the first Calloway to get schooling all the way through college so he thought he had to be strict on her, but he went overboard". He wanted the world for her, but "it was his dream, not hers...he never gave her time to pick it for herself". Angela Janet finally couldn't take her father's intractableness anymore, and ran off with one of the drummers in her father's band. This man, who never appears nor is named in the narrative, apparently is Bud's father.

Bud does find a home at the end of the story, with his grandfather, Herman E. Calloway, and his band (Chapter 19).