There's a couple of plumbing shops like that in town. A man started a biz in 1924, had some kids, remarried in the fifties and had another wife and another son. Two of the sons worked together until the dad died in about 1989 and the younger son left and started on his own. Of course there was a big stink about the younger son using the family name in his business and taking customers.
The older company uses the tagline, "Don't Be Fooled, the Original Since 1924" and the younger uses "A family tradition since 1924".
The older company uses mostly black trucks and has advertizing that says "Look for our BLACK trucks", while the latter uses only white trucks, but the older has started using a couple of white trucks. If customers ask "which trucks do you have, the white or the black?" they can say either way and get the others biz.