Tiger Woods' real, full name is Eldrick Tont Woods. That's what's on his birth certificate. The initials ETW are what Woods has used as the name of one of his companies, ETW Corporation.
There's no clear explanation of why his parents, Earl and Kultida Woods, decided to name their son Eldrick.
The middle name, Tony, however, was likely suggested by Kultida. Loosely translated to English as "beginning," Tont is a common Thai name and a nod to Kultida's Thai heritage.
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So, why the nickname Tiger? That's a nod to one of Earl Woods' buddies. Earl Woods served in the United States Army during the Vietnam War, and that's where he told people he met one of his best friends, a South Vietnamese soldier named Col. Vuong Dang Phong. Phong's nickname was Tiger, and Earl began calling his son that as an homage to him.
Earl Woods also referred to Tiger as "Sam," because he thought his son looked like a "Sam." Tiger named his daughter Sam.
Woods' nickname is just that, a nickname. Woods, as best we can tell, never changed his name formally to Tiger. Documents related to his divorce from Elin Nordegren refer to him at Eldrick Tont Woods.
There was some concern when Tiger Woods opened his The Woods Jupiter restaurant that Woods did not own the rights to use his own name, with the suggestion from a developer that Nike owned Woods' name. That's, in fact, not the case, with Woods able to not only use his name, but Woods also owns trademarks related to his name.