If they had married, would he have told her to change her name so he wouldn't having to "endure" proclaiming that "he loved Dixie"?
I don't believe it was anything like that. I don't think Duane was a liberal, but who knows? And "political correctness" was really not in vogue back in 1970. Plus, the Allmans were/are pretty proud of their Southern heritage.
I think Duane probably thought that "Little Dixie" might be considered insulting to the great land of Dixie.