Why do my classmates call me a descendant of Qin Shihuang when my surname is Qin?

In the historical Qin State, their monarch was named Zhao. In other words, Zhao is the surname because they also have an ancient surname "Ying". The Zhao family is actually a major branch of the Ying surname, so it can be said that Qin Shihuang's surname is Ying or his surname is Zhao, which is both correct. But it would be a joke to say that Qin Shihuang's surname was Qin, just like saying that Tang Taizong's surname was Tang, Song Taizu's surname was Song, and Yuan Taizu's surname was Yuan.

Generally, the monarch of a country will not have the same surname and country name. This situation only happened in the Chen Dynasty of the Southern Dynasties. As for using the country as a surname during the Spring and Autumn Period and the Warring States Period, it was only after the country was destroyed that the descendants of the public family would use the previous country name as their own surname. When this vassal state still existed, its monarch did not use a surname, so there was no reason for the monarch to use the country as his surname. What's more, the monarch of Qin already had a surname before the founding of the country, and there was no need to use the country's name as his surname. Only after the collapse of the Qin Dynasty, some royal nobles would change their surname to "Qin". Even so, the modern Qin surname is not a descendant of Qin Shihuang, because the mainstream Qin surname in China actually originated from a branch of the Lu State in the Western Zhou Dynasty, and the Qin family originated from the Qin State hundreds of years later than them. The status is also much lower and the numbers are much smaller. Qin Shihuang's own children all died in the court struggle, and there were no descendants to pass on, so the modern Qin surname can only be regarded as a branch of Qin Shihuang's relatives at most.