@envgen
In all seriousness I wonder if it's just that someone introduced them and said "these are doughnuts", as in the nut of a bolt, but made of dough, but someone heard it as "do-nuts" as in do-re-me ?

Or if it WAS doughnuts but over time bits of the word got shaved off, which means at one point they were called "dognuts"

@Nine @envgen the best bet for American English is usually Noah Webster, who intentionally simplified the spelling of a lot of words when he wrote his dictionary & is one of the major sources of difference between American and British spelling.

In the case of donuts, however, both spellings are actually originally American, as is the archaic ‘donnut’, and the three spellings likely just represent various local accents at the time of the words invention