right so imagine this. merlin's magic is revealed at some point during one of the early seasons and he's imprisoned by uther. but arthur helps him escape and they make a promise to each other that they'll meet again, that once arthur is king, merlin will return to camelot.
so merlin leaves and he sort of discards his name, takes on emrys. and then he starts learning magic. genuinely learning magic. he learns from kilgharrah and the druids and the catha and the sidhe and he travels a lot etc. and he's merlin so of course he starts making a name for himself. like he helps people and he accidentally ends up creating a sort of army in the process. he helps a dying man, now his whole village wants to fight for emrys.
basically everyone starts talking about him, this sorcerer from the legends called emrys, who goes around doing literal fucking miracles... he becomes something like a mysterious... god-like figure. everyone knows about him, even in camelot. he's supposed to be the most powerful sorcerer ever to walk the earth, after all. uther thinks he's a threat. morgana, like in canon, gets to know that he's her doom or whatever and she's even more scared of him than before
(btw he probably also has an apprentice . called mordred)
fast forward a couple of years, morgana and morgause are waging war on camelot, uther's dying, arthur is crowned. and the ceremony is about to end and suddenly arthur hears a long live the king! from a voice that he recognizes SO well...
so merlin and arthur meet again and they catch up on everything, morgana and uther etc [cue the new knights and courtiers being absolutely APPALLED by the way merlin talks to the literal king] and then arthur, in passing, mentions emrys. and that emrys might actually be a bigger problem than morgana if he ever attacked camelot
and merlin is like: ....er. arthur. hey. hold up
and he tells arthur that HE'S emrys
and then they win the war against morgana etc and yeah. happily ever after