What's the Difference Between Accent and Pronunciation?

Errol Spence Jr. is a former U.S. Olympian, a current titleholder in the welterweight division, and a rising star in the world of boxing. When announcers pronounce his name, they give it two syllables -- ERR-roll -- like the actor Errol Flynn.

But Spence is from deep in the heart of Texas. And he has such a drawl that, when he says his name, it's one syllable: "Earl."

So here's my question: If he pronounces his name "Earl", why isn't that just the right way to pronounce his name?

Put another way, we view him saying "Earl" as just an accented way of saying "ERR-roll". If I go to the south and pronounce things like a Yankee, they might find my strange speech amusing, but outside extreme circumstances they'd recognize we were saying the same words. An analogy might be if someone with a speech impediment said his name was "Yonny", we might still say his name is "Johnny." That said, if, say, an Israeli told us his name was "Dah-veed", we wouldn't use the American pronunciation of "David." There we'd simply say that name was pronounced differently, and it would be expected that Americans would say "Dah-veed."

So when is it one, and when is it the other? Genuine open question for the crowd.