Actually I would think that's a greater reason to have "Britain" be the dynastic title. I mean the Hannoverians are colloquially called the "House of Hannover" because they were the - surprise surprise - Electors of Hannover
But yes, Buckingham is a big nono, especially when it's a non-royal dukedom.
But on the contrary, if let's say William IV's descendants were the ones who had instituted the name change, perhaps the House of Clarence would be possible (or some other Duke of Clarence's descendant)


And yes, Wessex does sound the best, but I don't know if some may think that it relates too much to the word Saxon - and thus Saxony/Sachsen