It was named after Dinefwr Castle which was the court of the House of Dinefwr and one of the three principal royal courts of Wales with Aberffraw and Shrewsbury.
Eventually, a cadet branch of Dinefwr would establish itself in Powys by the mid 11th century, designated Mathrafal after the castle there.
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This branch would compete with House Aberffraw for supremacy and influence in Wales throughout the 10th, 11th, and 12th century, with Powys variously ruled between them.
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The FitzGerald dynasty and related families of Ireland are female line descendants of the Welsh royal family through Nest, daughter of Rhys ap Tewdwr, last King of Deheubarth, whose descendants include Elizabeth I, John F. Kennedy, and Diana Princess of Wales.
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Rhodri's second son Cadell ap Rhodri, however, looked outside Gwynedd's traditional borders and took possession of the Dark Ages kingdom of Dyfed by the late 9th century, establishing his capital at the citadel of Dinefwr.
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The south was restored to the Houses of Dinefwr and Morgan, but Powys and Gwynedd were given to Gruffydd's half-brothers Bleddyn and Rhiwallon.
The Prince of Gwynedd owed an honour debt to the House of Dinefŵr, as Gruffydd's father, Rhys ap Tewdwr, had aided Gruffydd ap Cynan in his own bid to reclaim Gwynedd from rivals in 1081.