The name Black Castle does not just apply to this particular spot, but includes the surrounding wooded area. The name does not appear on any maps, but many local people, particularly those of the older generation, will be familiar with it. See http://www.geograph.org.uk/tagged/Black+Castle#photo=3658133 for related pictures. This area is a
Image, long disused; see that link for further details.
[The second end-note has a link to an annotated satellite view: on that map, the site is indicated by a pale blue marker ("Black Castle") at the eastern extremity of one of the pale blue lines, near Carman Reservoir.]
Over the many decades since the quarry fell into disuse, it has become densely wooded and overgrown. As mentioned at the last-cited link, the way the quarry was worked has resulted in its having a terraced appearance in several places (see
Image), particularly at the eastern end, where the present picture was taken. Some of those terraces are fringed by low walls, the faces where the stone was worked; there is one such rock face at the centre of this picture, but it is overgrown with ferns and other vegetation.
The name Black Castle is at least a few decades old. However, before proceeding, I should stress that the explanation of it that I am about to give is speculation on my part.
As the area has been described to me, there are stones visible here (see, for example,
Image) and what looks like the foundations of buildings.
This being a quarry, there can hardly have been buildings here. However, the various terrace-like areas fringed with low stone walls may have suggested, to walkers passing through, the appearance of ruins, and this perhaps inspired the name Black Castle (possibly "black" because located in the shade of the woods). Decades ago, when the area was not quite so overgrown, those features would have been more clearly visible than they are now.
In short, the name Black Castle may simply have seemed an appropriate nickname; even those who coined the name probably did not seriously imagine that there had ever been a castle here.
Particularly at the western end of the former quarry, the construction of
Image in the 1880s, from the smaller pre-existing Carman Loch (which had itself been artificially created), is also likely to have left its mark on the area. For more on the formation of the reservoir, see the link just cited.
There are a few references to a "Carman Quarry" in older literature, but that name seems to refer to a later quarry, which is a little over a kilometre WNW of here, and which had its own set of traditions associated with it:
Image