I grew up in Mingo County.
I do not remember ever hearing of Mingo Mountain.

This is the "official" story:
"Mingo county was formed from a part of Logan county in 1895, and derives its name from the Mingo tribe of Indians, of which Logan was the famous chieftain. It was the last county to be formed in West Virginia"

A lot depends on where the collector, Jameson, got the song and when. If the source lived in eastern Kentucky my guess is that the singer simply assumed that Mingo Mountain was in some way associated with Mingo County which is right on the border of WV and Eastern Kentucky, across the river from Pike County Kentucky.

If the singer was from further west in Kentucky, my guess is that the singer had heard of Mingo County WV and made the same assumption. Mingo and Logan counties occasionally showed up on the national news during the mine wars. Mingo county would have been mentioned in any article about the "Matewan Massacre" for example.