This item was on the 06-2018 LoAR
3: Llewellyn Brydydd - New Name & New Device
Azure, a gauntlet fesswise grasping a drawstring bag argent
No major changes.
Language (Welsh) most important.
Culture (16th Century) most important.
Spelling ("Brydydd") most important.
http://www.s-gabriel.org/2254. leuan lloyd brydydd dated to 1406
"The last element in your name, <y Prydydd> means "the poet, the composer". The word <prydydd> was pronounced PR@-d@dh, where dh represents the sound of <th> in <this>. We have found several examples of this byname in period Welsh names:…Ieuan lloyd brydydd (1406) …Welsh occupational bynames normally do _not_ include the definite article <y> when they directly follow the given name of the person they describe; but usually do include it when they are used without the given name… Reference  Roberts, Glyn, "The Anglesey Submissions of 1406" in _Bulletin of the Board of Celtic Studies_, vol. XV pp.39-60."
Llewellyn in "Late Sixteenth Century Welsh names" by Talan Gwynek
Geiriadur Prifysgol Cymru http://welsh-dictionary.ac.uk/gpc/gpc.html has (s.v. "prydydd"), 1547 WS [A Dictionary in Englyshe and Welshe, ed William Salesbury, 1547], prydydd, a ryme maker. Amongst citations going from the 12/13C through to 1803. It also says: Fe'i ceir fel epithet, e.e. Meilyr Brydydd, leuan Brydydd, Hir. Cf. hefyd Prydydd y Moch, y Prydydd Bychan. [It is found as an epithet, e.g. Meilyr Brydydd (Maelir the Poet), leuan Brydydd Hir (leuan the Long Poet). Cf. also Prydydd y Moch (The Pig's Poet), y Prydydd Bychan, (the Little Poet)]
Concerning presumption, from Tangwystyl, via Adelaide:
Although issues of rank and status vary enormously across the medieval period, I'd be hesitant to set aside any of the various Welsh poetic bynames as making an inappropriate claim to rank. Let me put it this way: the early medieval Welsh laws list as a royal official the "court smith" who has a set of rights and perks associated with his office. But that doesn't mean that "smith" is a restricted indication of rank. There are several occupational terms relating to composition and performance that appear in the law tracts, including "pencerdd", "bardd teulu", "bardd cadeiriog" all with different duties and rights. The later poetic treatises (largely written at a time when all official function had ceased -- they were the intellectual games of independent artists -- mention a number of other terms and are far more interested in applying minute distinctions of rank than the law tracts were, at a time when they had essentially no authority to enforce those distinctions. But I digress…
There are a number of bynames meaning poet that appear during an era when they wouldn't have had any sort of legal status. The different bynames probably had distinctions of meaning for the people that used them, which we can only guess at from their historic connections.
Prydydd -- The literal meaning is "a maker, a composer". Famous examples tend to be associated with "the poets of the princes", that is, people whose recorded works were praise poetry for native Welsh rulers from around the 10-13th centuries. The byname may or may not have been understood as implying an official position--it may simply have been a description of their most notable achievement. Examples of prydydd as a byname can be found throughout the 13-15th centuries in contexts for people who aren't associated with courts (or when there were no courts to be associated with). It's found in both lenited and non-lenited forms. Morgan & Morgan's book on Welsh surnames has a discussion on reasons why lenition is variable (and why it appears at all) in bynames of this sort. The short version is that some bynames always lenite, some apparently never do, and some are variable.
Bardd -- This is, of course, the most recognizable of the bynames and one with a long history and broad use across the Celtic languages. When indicating what appears to be a formal position, it is typically modified in some way (bardd teulu, bardd cadeiriog, etc.). The late-period poetic manuals treat it as a formal rank, but as I note that was at a period when there wasn't actually any formal structure to apply it to. There are examples of bardd used as a byname by people with no special position in records of the 13-15th century. It appears in both lenited and non-lenited forms.
Clerwr - I don't have any examples of this as a byname. The poetic manuals treat this as the least prestigious of the poets, possibly even slightly derogatory.
I don't believe that "awenydd" was used as an occupational term in period (though I don't have my historic dictionary in front of me). It generally means the abstract concept "poetic inspiration".
So to sum up, if your client wants prydydd, that would be appropriate in meaning, is found as an ordinary occupational byname across a range of eras, and to my mind does not have any implication of rank or status when used all by itself. As it is found in both lenited and non-lenited forms in historic documents, he can probably pick whichever he likes. If you follow Morgan & Morgan's interpretation, it may be that the lenited form implies that you're distinguishing from someone else (which Meilyr? Meilyr the poet) whereas the non-lenited form is simply descriptive (Meilyr…you know, Meilyr the poet).