We were not very good about keeping our discussion on G2G and linked to the profile back then. There are some more off G2G email discussions that I think involved Isabelle, Jack Day, Doug Straiton, Lena, and some others. Isabelle was working on the profile that started the discussion and was the one who raised the issue. My participation was primarily on whether there was anything in Danish naming law or custom that would be in conflict with the EuroAristo guidelines.
From the Danish naming laws and customs point of view, there did not seem to be any reason to depart from the EuroAristo guidelines. The aristocracy was the first group to adopt heritable Slægtsnavn or family names and were required to do so by royal decree after 1526. Their slægtsnavn was usually the same as the house name. Anything else would probably have been considered a tilnavn (byname or discriptive name which could transfer to later generations and could be adopted as a slægtsnavn but wasn't required to be passed on). But you do have to look at each one individually as there was a sort of tendency to tack on more parts to form a more complex house name especially when someone married up to strengthen a claim or to broaden the scope of territory covered.
Everything I've looked at on Valdemar's father showed he clearly had a multipart complex house name and that would usually be inherited down to his son. The default in Danish naming law at the time of Prins Valdemar's birth was that children got the same slægtsnavn as their father had. Patronyms might still be some part of a name, but they would not have been the surname at birth.
I would be cautious about simplifying down to a single house name, especially without more support than what one person thinks the royal family calls themselves. Between a long period when Danish kings were elected and some recent Danish kings not having direct offspring, the Danish royal family veered off to some cadet houses or different house names more than once in modern history. Historical documents also indicate many Danish aristocrats with complex house names varied their use among the parts depending upon whom they were dealing with and how formal or informal a document was. So I would want some documentary evidence of intent to change the slægtsnavn before giving anyone a house name that differed substantially from the father's house name.
But I don't see anything in these points which conflicts in any way with EuroAristo guidelines, so I would just follow them.