It’s not an acronym. It isn’t traditionally capitalized, just a word: ham. Like the stuff you put in sandwiches.

My earliest understanding of it is that it started out when ham radio was brand new, and there was some rivalry between commercial radio and hobbyist radio. Commercial radio people started calling hobbyists “hams” with the same sentiment that applied to actors that overacted; they were aloso hams, of course. As to where that came from, I couldn’t say.