To really understand Why Branch? we should start at the start:
WHEN HE WAS A "MODEL" IN KOREA.
Brent is a perfectly fine given name that has never particularly suited him or his personality and he had long ago resigned himself to the name until one winter day in 2011, while visiting Brian Hunter, a friend who was then living in Gwangju, near Seoul, Korea.
Many hours and copious amounts of soju into Brent and Brian's visit, a man approached them and exclaimed, "I've been looking all over for a man with a beard! I'm a fashion designer — will you model for my catalogue?" Brent being Brent, he thought it might be a fun adventure, and agreed to go to a secluded area on a mountaintop in the middle of winter to model clothing that was at least three sizes too small.
When the designer asked for Brent's name, Brent answered:
"Sure. Yeah, Branch."
"And your last name?"
"I don't use a last name. It's just Branch."
Long story short, it turns out the man really is a fashion designer and Branch really was a "model" for a day in Korea. Ever since then, he's been known by some as Branch.