Because the surname represents birth, it means that the same female ancestor was born. "Shi" stands for identity, similar to modern official titles. If you have a surname, it means that you are a nobleman, a title or a fief. If you have a surname, you are just an ordinary person. For example, if you are from the countryside, from primary school to doctor, then I will call you Dr. Ji. And your fellow countryman just graduated from primary school, so I'll call him Ji Moumou, not Dr. Ji.