I think the hyphen helps keep the names together until it isn't needed because it is assumed that it should be said together. I don't know if your names work as double names, in my opinion because they have too many syllables and are more sophisticated names. John, Paul, & Anne are all one syllables and I think that makes it easier to pair them up as one ( even with the two syllable Marie)
I couldn't have said this better. I know a Mary-Katherine and no matter how much her parents tried it always got shortened to Mary-Kate or Mary-K (even MK). It was just too long. For double barrels to work in full in the long run they need to be short and sweet names.
I don't mind double barrelled names if they flow well. AnnaBeatrix is lovely with its 2-3 syllable count. The other two on the list are too long and both names end in "a". If you want both names, I would use a hyphen. People always seem to shorten two names to one.
I second this. And Anna-Beatrix is truly lovely. Furthermore, it's no longer than something like Anna-Maria, which most people would consider acceptable.