If we're talking post-game, the Queen has (in my mind) reclaimed her Garnet identity and would be thought of as such, though in moments of intimacy the playable party would likely call her Dagger (minus Steiner, and I imagine Beatrix never unbends that far.)

As far as the King of Burmecia, I suppose it's six of one, half a dozen of the other. We do know that Puck lived, so Burmecia has the option of being rebuilt. And I think Freya had decided to do that, had she not? It might also be that they were in a part of the city that wasn't as important to rebuild right away.