Black Rock farm, on the Bream road between Bream and Lydney, lies on top of the Colford High Delf coal seam. There are three other seams nearby; Trenchard, Whittington and Yorkley. They all out-crop within the area so would be a probable reason for the name of the farm.

There are no seams anywhere near Black Rock on the Severn but there is several out-crops of rock in the area and I think the name refers to one of those. There's another out-crop a bit further along called Black Bedwins. I suspect the 'black' in the name comes from the fact these rocks get submerged and are covered in seaweed. Have a look at this picture and you'll see what I mean. https://goo.gl/maps/9hVBa9TNRNu

So I don't think there's any connection between the names.