Okay, I emailed a marriage solicitor, and she said “if the hyphenated names occur from a previous divorce, either a birth name of one of the participants must be used, they must both keep their own birth names, or must hyphenate their birth names in conjunction. If both participants were born with their hyphenated names, then they may either hyphenate the entire series of names (although this is rare), adopt only one partner’s name, or select a single name from each partner’s name to be hyphenated. They may also, of course, keep their birth names.”
“If they wish to devise a name by other means, then they must file for a change of identity.”
Hope this helps. Only applies to the UK though.