I'm not a big fan of the name, because the "phrone" sound is not appealing to me. Knowing it's Greek improves it slightly, by giving the unusual sounds some context. I agree with the thoughts on pronunciation and similarity to a musical instrument (though it sort of makes me think of a harp).
However, I really like unusual origins for nicknames, so if I knew someone who was called
Sophie and learned their full name was actually
Sophronia, I would find that offbeat and an interesting bit of trivia about the person.