There is a long Chinese cultural preoccupation with having legitimate descendants who will carry on the clan line (that is, have the same surname as the father). This is expressed in Shang era bronzes from almost 3,000 years ago that I have seen in museums. The inscriptions on the cast bronze objects, which were often given as rewards to faithful subjects who achieved glory in battle or the like, include expressions of a wish to have children and grandchildren for countless generations.

The common saying is

不孝有三，無後為大

http://en.wiktionary.org/wiki/%E4%B8%8D%E5%AD%9D%E6%9C%89%E4...

indicating that the very worst way that a child can be disobedient to a parent is to not give the parent descendants.