The original name came about over where the famous ten yard seam of coal was mined. In places like Woodcross and Roseville it was near the surface and could be easily mined, sometimes by open cast.
In places like Baggeridge, Gornal, Pensnett and West Bromwich it was much deeper.
As well as coal, iron ore and fireclay was also mined and most of the pits were cheek by jowl with farm's and smallholdings, hence Black Country.
Later engineering towns adopted the name but that wasn't the original intention of the name.
Wolverhampton never claimed to be in it until it became fashionable.