They do, they just don't use them everyday. E.g. the Tudors were called the Tudors because that was their surname. Current lot are the Windsors I think.
Prior to that they were the Saxe-Coburg-Gotha's.[2]
[1]: http://en.wikipedia.org/wiki/House_of_Windsor [2]: http://en.wikipedia.org/wiki/House_of_Saxe-Coburg_and_Gotha#...