chandrika is a Sanskrit origin name. The chandra bit is probably a cognate of shine, and in Rgveda does mean that; but very quickly (i.e. from later Vedic period, at least) came to mean moon and soon became the common word for moon in Sanskrit. The -ika is a common suffix and means related to or child of, and then their is a suffix -A making it feminine. candrikA in the sense of moonlight dates at least to the time of the great poet kAlidAsa (last quarter of the first millenium or earlier), though chandrimA and jotsnA (both of which are also used as names, the latter from a root meaning bright) are more common words for moonlight.