https://en.wikipedia.org/wiki/Dixie
EDIT for those on a downvoting spree: I don't mean that the above meaning of Dixie is the origin of the Dixie Cup name, just that that's what I thought the original poster was referring to.
https://en.wikipedia.org/wiki/Paper_cup#Dixie_cups
As an American, Dixie cups are dixie cups :) I know, that's no answer but that was my intent, I do not think we use the term everyday and prefer to say paper cups, but if someone said "dixie cups" I would not be surprised, just like in some other places you could "xerox" a document instead of "photocopying" it.
Don't know how long off the boat they were, but often misspellings in UK surnames arise across generations in records. I guess because the family themselves are totally illiterate.
Also, IIUC on immigration to USA officials would record your surname on your papers and that became _the_ spelling, so that might also explain it?
Probably about a third of the people I meet pronounce my name wrong. It's a bit tiresome, but I wager if my name was Llywelyn it would be even worse.
The assumption that Americans anglicized their names did so by accident because they were illiterate is just silly. I'm sure that happened sometimes, but loads of people anglicized their names deliberately in an attempt to conform with local expectations. One of my great-great-grandfathers, a literate German speaking immigrant to America, changed his name from Müller to Miller. Why? Well I can't ask him, but probably because it was the thing to do. This sort of thing was very common particularly during that time period. The later means the same thing, sounds about the same, but crucially would be more familiar to anglophone Americans. And Müller is comparably easy.
(To be clear, my last name is not Miller; I have an non-anglicized but reasonably common Italian surname.)
My guess would be people not reading user names and assuming I'm the person who originally brought up the name.