They still are, the Dutch Royal family is still the House of Nassau-Oranje, the British Royal Family is still the House of Windsor (they were the house of Saxe-Coburg and Gotha until WWI when they Anglicised their name.)

It's a convention that dates from the 11th c Norman conquest in English.

Where the term is used to refer to earlier dynasties such as 'the House of Wessex' it's being applied retrospectively, they wouldn't have used it themselves.

It was essentially an alternative to a surname, the Normans popularised surnames in England but they weren't attached to family relationships at that point, they were only used to distinguish people from each other.

The concept of forming a surname by passing on the father's or mother's name (e.g the surname 'Johnson' meaning John's son) would have been known through contact with Scandinavian culture but it wasn't common in England at the time.

So you could be 'John of Bath' if you lived in Bath, but 'John of York' if you moved to York. Or you could be 'John Carpenter' if you worked as a Carpenter' but 'John Butcher' if you changed career to butchery.

It took a while, until the 14th c, for the idea of passing on a surname to your children to catch on amongst the lower and middling classes.

For noble and royal families however, the importance of showing who had the right to inherit from you and who owed you fealty was immediately evident. So their House names functioned as our surnames traditionally do today, they showed who a person was descended from or who a woman was married to.

Since then the convention has simply stuck, commoners have surnames, Royals and Nobles are members of Houses.