aww she's so cute, although she looks a bit like she's had an encounter with Banksy in the night, lol. Apparently it's a hybrid of her parents names Eclipse and Ulysses, to reflect her hybrid parentage. I guess they just made up a pronunciation, I would have said Ek-LIE-see too on first glance.
http://www.dailymail.co.uk/pages/live/articles/news/news.html?in_article_id=464723&in_page_id=1770