The Broads are different, I think. Looking at NPs like The Lake District, Peaks, etc. the 'heritage' is a bit smarter, more National Trust Shop in appearance, at least, that is my impression gained over visits. We are definitely scruffier and I am not sure how that plays in the NP ethos. Sure the broads, reedbeds, marshes and rivers are breathtaking, but the settlements certainly aren't up there with Matlock or Ambleside, so name or no name, some folk will not visit/revisit in the way they do the other NPs.
I can't see that a name change will have that much impact.
Better tourist facilities would help and these can only be provided through profitable businesses, so knocking efforts seems a bit counterproductive!
This is not to say, 'tidy away the boatyards' btw, they really matter; but I would happily lose the fish and chip shacks and Hoveton's awful 60s 'village centre'.