Haha, I think either name is fine just not together, for the Ave Mariiia reason.
Use Eva it's lovely, but with a different middle name.
Also- with Maria as a middle name, it's frequently traditionally used as a middle name for boys in spain and other countries, so I kind of irrationally worry that using it as a middle name will provoke taunts of 'haha you're a boy' for the child. Unlikely here though. Hmm...
Eva Marie? Eva Sofia? Eva Lucia? Eva Rizzo?