can be a Japanese name and it can be spelt with the characters for "night" and "rain". Theoretically new names can be created every day by Japanese parents and a lot of possible names probably haven't been used yet or are very rare. I wouldn't be surprised if somewhere in Japan there was a child called like this.
But the pronunciation would be a-ma-ya, so it's different from the basque name I think.
On the other hand, even if the name exists 雨夜 means "rainy night" and not "night rain" (eventhough the real precise understanding of the name is up to the parents as well)