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As regards names I would suggest Baptismal Family Clan as the trinominal system: Arthur Pendraig Auraidh = Arthurus Pendraconis Aureatorum = Arthur of the House Pendragon of the Clan Aureates (Auraidh = Euraidd = Aur(e)atus)

That sounds great!

The Auring title would just be 2: Caesar of the West & Imperator of Brittania/Britannia. Bretwalda is effectively a translation of the latter, it's a reduction of Breten Anwealda meaning Broad/Britain Sole-Ruler and became a common translation for Rex Britanniae.
The Coelings would probably just recognise the Imerador as High King, sometimes as just HK of the south, sometimes as HK of all the Britons (Aurlings and Coelings alike), depending on relative strength and recent wars.

Hmm I was intending that the Brythônys would view Bretwalda as a separate title, given by the English, with Imerâdôr/Âlt Rî being the one they gave Arthur several years later, but we can do both(sorta). They used to be separate titles in official documents, but by the 8th century they became the same title, just in different languages. I like your idea about how the Coelings view the title btw!

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