This is also a Japanese name, though rarely used and it can be given from the word rabbit, and it is commonly given during the year of the rabbit. It can also be built from the kanji "月姫", which translates to "moon princess".
Most Japanese people would not name a child "Usagi". In fact, some might even laugh (maybe quietly to themselves) if they heard that a couple had inflicted that on their daughter. [noted -ed]