There seem to be dissenting opinions on this, but perhaps during the time of his rule he did convince the ancient Nords that he was Akatosh and that's why the notion persisted.
The problem with that theory is that Akatosh (as we know him) wasn't created until Alessia's rebellion in the first era, when she created the Imperial pantheon as a compromise between the Elves' and Nords' pantheons, whom already held Alduin as a god. How could Alduin convince Nords he was the god Akatosh, when Akatosh wasn't known to people yet?
My theory is that Alduin very much is a god/The World Eater. Notice that even among dragons, he's special. Dragons can be killed without Dragonrend, but Alduin can't even be injured without it. And even when you wear him down, he doesn't die, he just goes off to eat souls and get strength back. It's only when you wear him down in Sovngarde that
something strips off his divine shell and takes his soul.
Alduin is the end and beginning of time. He was there at the beginning, and even at the end of the MQ, Angier and Paarthurnax say he'll most likely be back when it's his time to be. But early on in the Dawn and Merithic era, before time fully stablized, he 'lost his way' and tried to take more power for himself, aspiring to also be the preserver and stabilizer, whom he wasn't. This is what got him kicked in the tail in the early First Era by Akatosh, who rightly belongs in that role.
I'm not really sure of the timing of that, though, when Alessia created Akatosh and how that coincides with the Dragon War. But it at least fits the timeline better than "Alduin is just a normal dragon who pretended to be the Time God Akatosh to the ancient Nords" since the only other Time God back then was Auri-el, an Elvish god whom the Nords would reject on principle of being Elvish.