I've asked this question directly to my friends; it's also very common amongst Koreans, but strangely uncommon for the Japanese to do so.
Some names simply don't survive moving between languages. A Chinese name for example may be too difficult or strange to use around English-speaking people. Also, an attempt by an English speaker may ruin the tones and even change the meaning of the name (this happened to a Chinese friend - bad pronunciation of her name by non-Chinese gave her name a negative meaning. She quickly adopted a more European name).
The other reason is it's more comfortable to adopt a name from your second language so it doesn't feel like you're code-switching. I've also adopted an individual name in Chinese with its own meaning (instead of transliterating my name) - you'll often find westerners who learn Chinese do this.