This Chinese charater 月 could mean moon, moonlight and month. In the Chinese culture, moon could symbolize reunion, longing, purity and beauty. People usually use an adjective 皎洁 to describe the moonlight. 皎洁 could be translated as bright. And you could find that there are males and females whose first name, I mean, their given name, is 月.
For instance, Shen Yue, or 沈月 in Chinese, an actress from mainland China, Cao Xiyue, or 曹曦月 in Chinese, an actress from mainland China, Xu Lingyue, or 许龄月 in Chinese, an actress from mainland China, Guan Shanyue, or 关山月 in Chinese, a painter from mainland China, Tao Lengyue, or 陶冷月 in Chinese, a painter from mainland China, Jing Yaoyue, or 景耀月 in Chinese, an educator from mainland China.
Here is a picture of Shen Yue.
Here is a picture of Cao Xiyue.
Here is a picture of Xu Lingyue.
Here is a picture of Guan Shanyue.
Here is a picture of Tao Lengyue.
Here is a picture of Jing Yaoyue.
So, as you see, 月 is used as a unisex given name.