EFRDDYL (standardized modern form)
While Nyfain and Gwawr married into the Rheged aristocracy, and so we can at best say that their names are ones that may have been used in that context, the two women in the next generation were born into that family, so we can postulate that their names represent ones current in that culture.
Efrddyl is said to be the twin sister of Urien Rheged, giving her a calculated date in the early 6th century. While it's true that twins sometimes run in families, enough pairs of twins are attributed to this particular royal line that some skepticism may be called for -- especially when other mythic elements appear. Efrddyl's three children are said to be triplets, including a daughter Ceindrech (or in one source, Arddun).
Textual Sources
Euerdil - De Situ Brecheniauc (Cotton ms. Vespasian A xiv, fos. 10v-11v (ca. 1200) text perhaps a century earlierErduduyl - JC MS 20 written late 14th c., copied from ms ca. 1200; this is not so much a corruption of the name as a substitution of a similar-sounding name -- there are several examples of the feminine name Erdudfyl in legal records of the late 13th century (e.g., the 1292 Lay Subsidy Roll for Meirioneth and Cilgerran)
Evrddyl - Plant Brychan
She is mentioned in the triads (Bromwich TYP no. 70) as having one of the "three fair womb-burdens" of Britain. In various versions, her name is given as:
[...]dyl -- (the text is evidently incomplete) Peniarth Ms. 47 (15th c.)Eurddel -- Peniarth Ms. 50 (first half of the 15th c.)
As Urien's sister, she also rates two mentions as mourning her brother's death in the poetry associated with Llywarch Hen (Williams CLH, Ford PLH). The text is from the Red Book of Hergest, created ca. 1375 but with material copied from earlier sources. Her name appears there as Euyrdyl and Eu[y]rdyl (i.e., in the text as Eurdyl for the second), which are consistent with the date of composition or the couple centuries previous.
This personal name also occurs for the mother of Saint Dubricius (second half of the 5th century). The Book of Llandav (Bartrum WCD) mentions several places named presumably after her, in documents tentatively dated around the 8th century:
insulam ebrdil (island p.76, charter 76a, dated ca. 575 but of questionable historicity)Euirdil (river p.78, charter 77, dated ca. 625 but of questionable historicity)
euyrdil (river p.78, charter 77)
(as marginalia in charter 77, we also see Eurdila' with a t erased over the a, and Eurdila with a macron over the a where we might expect a Latin accusative ending in -m)
The life of Dubricius is in a 15th c. hand:
Ebrdil (dau. of Pepiau p.78-9, life of Dubricius, the b was later altered to u)
inis ebrdil (island p.79, 80, life of Dubricius)
(as marginalia on p.79 we also have ynys evrddyl)Lann Efrdil (church p.159, charter 159a, dated ca. 685 but of questionable historicity)
(as marginalia on p.159 we also have llann eurdyl)finnaun efrdil (river p.173, charter 171b, dated ca. 860)
Lann Ebrdil (church p.192, charter 192, dated ca. 745 but of questionable historicity)
aperfinnaun emrdil (river p.264, charter 264a, dated ca. 1030)
aper finnaun efrdil (river p.264, charter 264a, dated ca. 1030)
Linguistic Analysis
Here we have some nicely useful early forms. Despite the conflict between the b and m forms, the b strikes me as being the more reliable. The second syllable in the tri-syllabic forms is epenthetic and may be discounted when reconstructing. Furthermore, the r, dd, and l are relatively unproblematic in reconstruction. The initial vowel has several possible originals, partly dependent on the lost vowel in the first half of the name. (The existence of such a vowel is much more likely than that the cluster -brd- was original, although in theory it could occur either after the b or r.) If the lost vowel caused i-affection (Jackson p.579ff), then the initial vowel could have been any of a, e, u. If the lost vowel caused a-affection, then the initial could have been i (Jackson p.573ff). If the lost vowel caused no affection, then the original initial was presumably e. The only remotely similar Brittonic name that comes to mind is the Romano-British Eburacum (York), but there is no positive basis for assuming any sort of connection between the two names.
We can't dodge the question, because in this woman's lifetime, vowel loss would not have occurred yet in written forms (although it was likely well progressed in speech). So we're left with offering a number of incomplete possibilities for written forms (assuming the standard Latinate feminine ending -a):
*abirdila*abridila
*ebirdila
*ebridila
*ubirdila
*ubridila
*ibardila
*ibradila
*ebVrdila (where V=e, o, u)
*ebrVdila (where V=e, o, u)
For a spoken form, if we take an optimistic view of the earliness of syllable loss, and taking into account lenition, then the only real uncertainty is the initial vowel. Using, just as an example, the "e" possibility, we would get something like: ['EBr-DIl] or, in English syllables, "EVR-dhill" but where the "v" is made with both lips and the "dh" represents the initial sound of "then".
As it happens, there is also a common noun in Medieval Welsh of the form efrddyl, the irregular plural of an apparently rare word afrddwl meaning "sad, unfortunate", or as a noun "disappointment, misfortune" (GPC). It would be precipitate to conclude that the personal name actually derives from this word, however it offers a way of resolving some of the multiple possibilities. The derivation offered for afrddwl suggests a Brittonic *ab(a)r-dall- and for the plural *ab(a)r-dalli. There are some problems with this reconstruction if the (a) is included, so we shall omit it. This would give us a 5th c. written form of Abrdalli and a pronunciation along the lines of ['aBr-Di"l], or in English syllables "AHVR-dhi"l" where i" represents a vowel like schwa but higher in the mouth, and v as above.