ANGHARAD (standardized modern form)
According to the triads (Bromwich TYP no. 79), Rhydderch Hael had a daughter Angharad Tonfelen (the byname appears to mean "yellow wave", possibly in reference to hair); whether she was the daughter of Languoreth is not mentioned specifically (although a son is specifically attributed to her). Based on Rhydderch's assigned date, she would presumably belong roughly to the late-mid 6th century.
Excluding individuals with purely legendary connections, she appears to be the earliest known instance of the name Angharad, although Bartrum (WCD) lists a near explosion of women with the name in the 9-10th century, and it was extremely popular in the later medieval period.
Angharat Ton Velen -- Peniarth Ms. 47
The earliest example of the name itself that I can locate is:
hancarate (a Latin genitive -- the root would be hancarat) -- in a ca. 9th c. marginal note in the Book of Chad (Jackson LHEB)
This name is generally agreed to derive from an intensive prefix an plus an element based on the root car "love", with a composite meaning "well-loved". Taking this derivation as accurate, the 9th c. form in the Book of Chad seems likely to be good for the late-mid 6th c. as well: Ancarata, pronounced something like [aN-'kar-ad] or, in English syllables, "ang-KAHR-ahd". (Normally, we'd expect the accent at this date to fall on the first syllable, but here the first syllable is a grammatical prefix that would likely not take the primary accent.