NYFAIN (standardized modern form)
For general background, see the comments on her supposed sister Gwawr above. Nyfain is said to have married Cynfarch Oer ap Meirchion Gul, and was the mother of the twins Urien Rheged and Efrddyl. (Cynfarch has other attributed children -- see e.g. Enynny below -- but Nyfain is not explicitly given as their mother.) Her name appears in early lists of Brychan's children in the following forms (Bartrum EWGT).
Neuein - De Situ Brecheniauc (Cotton ms. Vespasian A xiv, fos. 10v-11v (ca. 1200) text perhaps a century earlier
Nyuen - Cognacio Brychan (Cotton MS. Domitian I, fox. 157v-158v) ms. dated 1502-55, copied from a ms poss of the 13th c.
Drynwin - JC MS 20 written late 14th c., copied from ms ca. 1200, although the family relationships given for this person match those for Nyfain, it's hard to see how the name could be corrupted in this way
Nevyn - Plant Brychan
Another possible example of the name in South Wales (although there is no indication that it is for the same person) is the dedicatory saint of a place mentioned in the Book of Llandav as Villam Sancti Nuvien and Lann Uvien (presumably a reanalysis of Lan Nuvien?) (Bartrum WCD). The latter is from a charter given a tentative date in the late 8th century (Davies EWM). The same location is given in a 1336 document as Sancti Nyveyn al. Niveyn (Bartrum WCD).
Despite the variant form of the diphthong in the second syllable in some of the Llandav material, the evidence as a whole suggests a standardized form of Nyfain (Medieval Welsh standardized form Nyvein), with occasional reduction of the diphthong. None of the citations are early enough to reveal whether the radical underlying the f is m or b. It is tempting to try to connect the first syllable with *nem "heaven, sky" (GPC). It is tempting to try to connect this name with the second part of the masculine given name Ednywain. There are occasional examples of conversion between v/w (in both directions -- see further under Morfudd below), and the initial part of this name appears to derive from *Iud-, similarly to the names Idnerth/Iudnerth, Ithel/Iudhael, Iudnimet/Ednyfed et al. (Morgan & Morgan tentatively suggest that Ednywain derives instead from a cut-and-paste of Ednyfed and Owain, but this sort of recombination that cuts across known thematic elements is a very unsatisfactory hypothesis.) This connection, however, doesn't help in reconstructing an early form, as the masculine name survives only in medieval examples.
The ns may be taken as original, being astonishingly stable among all the changes of the language. If we take the original of the middle consonant as m without assuming a particular derivation, then the first syllable reconstructs as either *nem or *nim (Jackson p.278ff), but if the latter, then we would expect a change to nem by the 5th century. While the m would have begun lenition at this date, it was still strongly bilabial and nasal, but moving from being a stop to a fricative. The diphthong in the final syllable must arise from a simple vowel via some sort of vowel affection. The most likely candidate for this particular result appears to be something like -ani-. Inscriptional evidence suggests that this vowel affection was at work in pronunciation by the end of the 5th century, although it is only very rarely indicated in written forms at that time (Jackson p.579ff). If so, this would presumably derive originally from a feminine ia-stem declension, although Latinized written forms of this period appear to treat all feminine names as regular a-stem nouns. This woman lived roughly during the period when syllable loss was occurring, so we can assume that the inflectional ending would be much reduced, but perhaps still pronounced.
We can then suggest a Latinized written form of Nemania and a pronunciation something like ['neB~-ajn-j@]. Or, approximated by English syllables, "NEV-ine-yeh" but where the "v" is made with both lips and is nasalized.