Was there a name for the band that played with Brisco Darling?

In real life, The Dillards.

On the show, they were just members of the Darling Family.

yea, they're a bluegrass group and as far as I know, they're still around.

In the first episode that they were in, Earl Hagen (who wrote the show's theme song, and did the whistling on it) appeared with them in one scene.