What is the most common name, first and last, in the world?

The answer to this question isn't easy to determine because countries have varying amounts of data available, and that data often doesn't come out at the same time. The following is the best guess we can make:

Zhang Wei appears to be the most common full name in the world. This was stated in a Beijing News article, "One Name 'Zhang Wei' Covers 290,000 People", 26 Jul 2007.
https://en.m.wikipedia.org/wiki/List_of_common_Chinese_surnames
http://www.chinawhisper.com/top-50-most-common-chinese-names/
Mohammed is the most common first name in the world. According to the sixth edition of The Columbia Encyclopedia (2000), Muhammad is "probably the most common given name" in the world, including variations. It is estimated that more than 15 million people in the world bear the name Muhammad.
Some variations: Mohammad, Mohammed, Mohamed, Muhammed, Mahommed, Mehmed, Mehmet, Mahomet
https://en.wikipedia.org/wiki/Muhammad_%28name%29

The name Muhammad wins the prize for the world’s most common name. It derives from the Arabic root “h-m-d” and means “praiseworthy one.” It’s often used, much like John Doe, to indicate someone whose name is unknown, or in combination with another given name.

pitlanemagazine.com/morals-values-and-norms/muhammad-the-most-common-name-in-the-world.html no longer exists
https://www.gulmiresunga.com/2011/08/most-common-name-in-world.html
Li / Lee is the most common surname in the world. Zhang is close.

China hosts the three most common surnames because it is the country with the largest population in the world. Li and Lee are the surnames of over 100 million people of Chinese, Korean and Vietnamese heritage. The name derives from the Chinese word for "plum tree"; the name was popularized by the emperors of the Tang dynasty that used it. Zhang is also a surname for over 100 million people of Chinese origin.

https://www.reference.com/education/10-common-last-names-world-ff45abb098a0454b
This site orders Li, Zhang, Wang, Nguyen, Garcia
http://www.angmohdan.com/angmohs-last-name-lee/
Smith is the most common surname in the English language, with over 4 million bearers across the world.
https://www.reference.com/education/10-common-last-names-world-ff45abb098a0454b
Breakdowns by country:
https://en.m.wikipedia.org/wiki/Lists_of_most_common_surnames

The most common family name is LI, a book published today SURNAMES IN CHINA reports that there are 95 million living in China with another 5 million worldwide.