Before the Qin dynasty, surnames were not combined, surnames were surnames, surnames were surnames. The two are different. The surname is big and the surname is small. Surnames are used to distinguish marriage. People with different surnames and people with the same surnames can get married, but people with different surnames can't get married, because they are children of the same family, and marriage is likely to lead to genetic diseases.
Surnames are used to distinguish between high and low. People with prominent positions can choose their own surnames, so even in the same family, surnames are different. A woman takes her husband's surname. For example, your surname is Wang now and you have three sons with your wife. When these three sons grow up, everyone has different social classes, including the rich and the poor. Then rich people can change their surnames, but their surnames are still Wang, just different from yours.
So, for Qin Shihuang Ying Zheng, he got the surname Zhao. The surname won can be traced back to the ancestors of Qin Shihuang. Zhao knows this very well. Qin Shihuang's mother called, because his wife took her husband's surname, Qin Zhuang, Qin Shihuang's father, was Zhao. Being an emperor is noble enough. Taking Zhao as the surname shows that Zhao is really noble. When you arrive at Qin Shihuang, you naturally don't have to choose a surname, just follow your father's surname.
As for Fu Su and Hu Hai, their surnames are Fu, Hu, Fu and Hu. Because Qin Shihuang unified the six countries, Qin Shihuang unified writing and trade, and even unified surnames. In order to carry out the New Deal, he and his sons naturally set an example. Qin Shihuang thought he was over half a year old, so there was no need to toss about. But the sons are still very young, so it is very likely that Qin Shihuang gave them their surnames.