Maelgwn wasn't automatically the ruler upon his father's demise. Celtic society didn't work like that. The chieftain was the strongest person for the position, though in reality that tended to be the son - or a relative - of his predecessor.
Nevertheless, Maelgwn couldn't legally rule as an avowed monk. Then again, who was going to stand in the way of this military leader of proven prowess? As soon as Maelgwn renounced his monastic oath, we can be certain that it was game over for any other erstwhile chieftains.
Cadwallon had established the llys of Gwynedd in Aberffraw, on Ynys Mon. But Maelgwn disdained that for the fortress in which he was (probably) born - Deganwy. It dominated the entrance to the Conwy sea-port, but on the other side of the river. In short, Maelgwn made his base just over the border in Rhos.
This was the eastern territory of the Votadini ruled not by Maelgwn, but his uncle Owain Ddantwyn, then his cousin Cuneglas. From the very start, it seemed, the Gwynedd ruler was determined to become overlord of his great-grandfather's entire realm - Rhos and Gwynedd together. Lands which covered the whole of North Wales, taking in Chester too, all the way to the east. Curtailed at Ceredigion and Powys in the south.
In doing so, Maelgwn would become probably the most powerful Celtic chieftain in Britain. His prominence, and that of his territory, would append the suffix Gwynedd to his name. Even the Saxons would refer to him as 'the Great'.
And to signify his elevation, he took the title Pendragon and the symbol of a dragon became his emblem. Some historians relate it to the last banner of the local Roman legions, who had abandoned Gwynedd a century before. Others to the Celtic legend of a red dragon uniting the Britons. Arthurian scholars see it as a borrowing, taking on Arthur's position in the wake of Camlan. It may be all of the above.
Maelgwn Gwynedd's dragon would eventually evolve into Y Ddraig Goch, the icon of the Welsh.