I just Googled the Swedish-Japanese guy in the OP, and according to this interview, his Japanese name was given to him by the master gardener he was apprenticed under:
“The family name ‘Murasame’ was given to me by my master. The given name ‘Tatsumasa’ is a combination of ‘dragon’ (tatsu), the [zodiac] year when I was born, and one character from my master’s name,” says Murasame."
So I think maybe it's less like naming yourself 'Brandon McFreedom' and more like moving to the states to work under a veteran car mechanic named Bud McLean, and then having him turn to you after a few years on the job, and say "Son, it's time for you to become an American so you can open up your shop. And when that day comes, I think the world should know you by a new name: McLeo GM Corvette."