given name

Now, from behind the name: I didn't find Ellone from there, so obviously it's not a very common name or doesn't have a specific meaning. I did find her pet name though, Elle.
They say it's short for Ellen (medieval version of Helen) and can be given 'in referance' of the French pronoun elle, which means she.
....if anyone still thinks Ellone is a boy, don't do that anymore. It's all in the name.

surname

Some people think Ellone's last name is Loire (I'm one of these) and some think it's Leonheart. I don't personally know which one is right, but after thinking about it for a long time I've come to the conclusion that Leonheart is the right last name for her (even though Loire sounds better, imho). Why? Let me count the reasons:

01. Ellone calls Laguna Loire "Uncle" instead of "Dad", although later he becomes Ellone's adoptive father.
02. Raine adopted Ellone before Laguna came into the picture, thus giving Elle her own maiden name.
03. Although Raine later took Laguna's last name after getting married, she still named Squall a Leonheart, not Loire.

It is also possible that Ellone took Laguna's surname with Raine or kept her real parents' last name (if she knew it, she was so small), but we will never know that. In the game she just goes by the name of Ellone.