1. The ancient Chinese people have 2 names, one is called 名，another one is called 字。For example: 诸葛（surname）亮（名first name），孔明（字another name）；关羽（名），云长（字）。So, 名字 originally means 名 and 字。This tradition had been fading along of the revolution in the early 20th century, the last China emperor was forced to abdicate, Republic of China was established.
2. Chinese women don't change their last name after marriage. So, don't mix up married woman's last name with her husband's last name.
3. Most of surnames are single character, only few are double, like : 诸葛，司马，慕容，欧阳，etc.