Page "Qin Shi Huang" Paragraph 13

According to the Records of the Grand Historian, the first emperor was born in 259 BC as the eldest son of King Zhuangxiang of Qin.

King Zhuangxiang of Qin saw a concubine belonging to Lü Buwei, and she bore the first emperor on 18th of February, it was in January according to the Chinese calender.

At birth, he was given the clan name of Zhao ( the clan name of the royal house of Qin ) inherited from his father and personal name Zheng ( 正 ), because he was born in the first month ( Zhengyue 正月 in the Chinese calender ).

His clan name Zhao has nothing to do with being born at the Kingdom of Zhao, it was a coincidence.