What is Billie Eilish's real name?

Can you please clarify for me the actual name of the singer Billie Eilish? I understand she's a popular artist in the music industry, but I'm curious about her birth name and if it differs from the one she's widely known by. It's quite intriguing to learn about the origins of an artist's name, especially when it's as unique as Billie Eilish's. Could you provide me with the answer, perhaps alongside any insights into why she chose to go by this particular moniker?