"Historical Records of the First Qin Emperor" records: "King Qin Zhao was born in Handan in the first month of forty-eight years. Jisheng, named Zheng, surnamed Zhao. " In other words, Qin Shihuang was born in the first month of forty-eight years, hence the name "Zheng".
Later generations also have many explanations for this. Guangxu's explanation in the Collection of Historical Records is: "First, it is' positive'." That is, "righteousness" and "politics" are interlinked. Zhong Song's explanation is: "Born in the first month, so the name is correct." The explanation of Historical Records is: "This is' Zheng', born in Zhao, so it is called."
There are actually many statements about this Zhao Zheng. One theory is that the original name of the monarch of the State of Qin was Zhao (see Historical Records of Qin Benji), so it was called "Zhao Zheng"; One theory is that he was born in Zhao, so he is called (see Historical Records); There is also a saying that his mother named Qin Shihuang lived in Zhao when he was a child, so he was named because he was afraid that his surname would be won by Zhao people. Anyway, there is indeed Zhao Zhengyi.
Therefore, according to historical records, the name "Zheng" is related to his birth time.
As for other statements, I won't list them unless they are in the history books.