Neigwl (Neugyll 1291, Newgwl 1352) was the centre of the commote of Cymydmaen, for which Porth Neigwl would have provided important sea access. The origin of Neigwl is rather obscure but is probably a personal name, perhaps Irish or old Norse.
References include:- Nygull C16, Porthnegoll 1561, Porth Nigwl 1629, Neigwi or Hell's Mouth 1805, Porth Neigwl or Hell's Mouth 1816.
Neigwl may be of similar origin as the English Newgale.
From where did the mutilation "Port Nigel" come? Is it from Bennett & Vernon 2002? It has certainly raised a few laughs!!