Feelings don’t change facts. The House of Oldenburg is German in origin; in such houses one is a member of the house one’s father belonged (if of legitimate birth) going back as far as one can trace. “Changing” a house’s name only effectively creates a cadet branch.

The Glücksburgs didn’t change their house name upon ascending the Danish throne. They already existed as a cadet branch of the House of Oldenburg. There was no decree to change their name. It was simply just a fact as being descended in a legitimate male line from the dukes of Glücksburg of the House of Oldenburg.

Elizabeth II is not Queen of England; she is Queen of the United Kingdom and fifteen other realms. Her descendants are members of the House of Windsor, their branch being a line of the House of Glücksburg, which is a branch of the House of Oldenburg. None of her descendants are Coburgs of the House of Wettin because none of their fathers are.

House names were not generally decreed because they happened as a matter of fact of male line descent and they automatically changed when the male line did.