The Spanish equivalent of English idyll is égloga, but the Italian equivalent is idillio, so it is possible that parents thought that this word would sound beautiful on their son (Idilio) or daughter (Idilia). It wouldn't be the first time parents had named their child something that was previously a word only.
"How do you pick up the threads of an old life? How do you go on... when in your heart you begin to understand... there is no going back? There are some things that time cannot mend... some hurts that go too deep... that have taken hold." ~ Frodo Baggins