The cave in question was called Ogof-y-Daren Cilau by the Caves of South Wales, guidebook of 1978 et seq, which is where cavers got it from although BNSSS is credited with the discovery in 1957.
The name Darren Cilau is used on OS 1:25000 and 1:50000 maps for the quarry behind Whitewalls (not the next quarry towards Brynmawr with the eponymous cave entrance) and much further along the same escarpment is the "Craig y Cilau" national nature reserve with more caves like Agen Allwedd.
Tarren / Darren is the Welsh word for an escarpment, which is a pretty accurate description for this locality, and a glance over the local OS map shows plenty of other rocky Darrens. Welsh doesn't double many consonants, the common ones being N and R, and it also has an un-doubling feature too, as in tarenni which is the plural form. Not to be confused with dd and ff and ll which are treated as single letters. A dictionary lists all the E- words followed by all the F- words, then the FF- words!
But what does Cilau mean? Cil means a small corner recess, as in corner of the eye or corner of the jaw, and the plural is ciliau not cilau. I suppose it could be referring to the two right angle corners in the escarpment known to cavers as "Windy Corner" and the sharp turn at Elwys Faen which are met while walking the track to Aggy, but these are huge corners, and otherwise it seems a bit odd to call an escarpment like this cornered. The usual word for big corner in Welsh is cornel.