Chen's name, "橙", can be literally translated as "bitter orange" in the Japanese Language, but the Chinese characters would be translated as the color orange. All of the Yakumo family are named after the names of color. Why Chen appears before Ran and Yukari comes from the fact that the orange light has physically lower energy than the indigo, Ran, and the violet, Yukari.
The pronunciation of her name, "Chen", is derived from the obsolete Chinese reading of 橙. In Japanese, that character would be read as "tou" or "daidai"; in modern Chinese, "cheng".
She is one of the few Touhou characters in the Windows series to not have a last name that is specified. (Others being Cirno and Kisume, for example.) However, it can be assumed that her last name is Yakumo.