Conversation so far:
When did the reign begin?
The kingdom of Gwynedd began with the reconquest of the coast by northern Britons.
Who were the Britons fighting?
Gaelic tribes from Ireland.
How did the conquest go?
Generations later, Maelgwn's father Cadwallon Long-Hand completed the process by destroying the last Irish settlements on Anglesey.
Who started the conquest?
Maelgwn's great-grandfather Cunedda Wledig.
Where did the name Gwynedd come from?
He is thus most commonly referenced by appending the name of the kingdom to his own: Maelgwn Gwynedd.

Question: When did his reign end?
Self-contained rewrite: When did the reign of Maelgwn Gwynedd end?