Wikipedia confirms the above story about Rod Brasfield of the Grand Ole Opry, who had a ventriloquist's dummy called Bocephus.

There is a formerly well-known comical song BOHUNKUS a.k.a. BOHUNKUS AND JOSEPHUS, about two brothers with those names. I suppose Brasfield invented "Bocephus" by combining "Bohunkus" and "Josephus."

So where did "Bohunkus" and "Josephus" come from?

Josephus was an important Roman-Jewish historian from the 1st century A.D. (Of course there have been other people with that name, but the historian is the most famous.)

"Bohunkus" is probably a made-up name invented by whoever wrote the song. It is probably based on "bohunk," a pejorative slang term probably formed from "Bohemian" and "Hungarian" and formerly applied to immigrants of Eastern European origin.