In China there is a very famous Canadian by the name of Mark Rowswell dashan.com. One of the reasons he is so famous in China is that his Chinese is very very good. His adopted Chinese name is 大山 (dàshān) which means great or large mountain.
Several years ago I decided to also adopt a Chinese name. One day a name popped into my mind. Mark's Chinese is very good but my Chinese is only basic. Consequently, I chose the name 小山 (xiǎoshān) which means little mountain ☺
An advantage of having an adopted name is that one can change it and I can change it to reflect my progress in mastering the Chinese language. So as my Chinese improves I can change it to 中山 (zhōngshān) which means middle mountain. Then 大山 (dàshān) and finally, if I ever reach this level of proficiency, 巨山 (jùshān) which means gigantic mountain.
There are though, some days when I think my Chinese is so poor that maybe my adopted name should be 微山 (Wēishān) as this means micro mountain.