Interesting, I didn't realise that was a thing in the States too (http://english.stackexchange.com/questions/22446/lunch-vs-dinner-vs-supper-times-and-meanings). I thought it was only the oddballs here in Yorkshire who say dinner at lunchtime! :D But looks like Vietnamese specify meal names based on time of day rather than meal size.
I grew up and live in the South. That might occur in VERY rural places, or more likely long ago, and if so, it's very atypical, but I've never heard of that personally or seen that in any sort of movie. I would say that supper is a more Southern and colloquial term for dinner.
I live in Nebraska, and ‘dinner’ is still used for the noon meal on the farm, but not in town. I live in Lincoln (which passes for a big city here), but my dad grew up eating four meals a day: breakfast, dinner, lunch, and supper. Noon dinner is the big meal, eaten at the house if possible; lunch is a small meal of cold leftovers or a sandwich, usually eaten in the field; and supper is another small meal, eaten back at the house shortly before bed. (And breakfast is just breakfast, although you have to feed the cows first.)