Chinese person here! Many of my relatives who were born/raised in China or Taiwan have self-selected Western names, so it's not too uncommon to see that. I'm not so sure about the other way around, though. I have some non-Chinese friends who've studied abroad in Chinese-speaking regions, but I don't think they ended up adopting a Chinese name.
The Chinese word for "free"—as in being liberated or independent, which I'm guessing is what you mean?—is 自由 (zìyóu). (I don't think it's commonly used as an actual name, but do as you wish with it.) Also, two-syllable names aren't necessarily random. Most names have auspicious or positive meanings based on the characters chosen, so you wouldn't just throw any two characters together. Theoretically, the possibilities are endless if you disregard this custom.
This message was edited by the author on March 29, 2020 at 12:26 PM