Although not of the same origin, the Hebrew female name Chen (khen, hen, khehn, spelled חן in Hebrew) means favour, grace. They are both anglicized the same way, so I thought I'd add that bit of information! Both have very nice meanings.
I'm afraid people need a disambiguation here. Because of the meanings of Chinese Characters are defined by how they were written, but not pronunciation. So, many words may share the same pronunciation and same spelling in Pinyin system.This is one case. The character "晨" truly can be used as a given name. But two other character "辰" and "陳" which have the same spelling "Chen". "辰" is used as given name, it is the fifth of twelve earthly branches, also mean daytime, star and use as a variant of "晨". [noted -ed]"陳" is an surname widely used in China, especially in the Southern part.
Beautiful and simple. I wish Chinese names would cross over into Western naming; I'd feel stupid using a Chinese name without any Chinese heritage, but so many are so very pretty.