Namaste.
It is no more a symbol of Shiva than a picture taken of you is a symbol of you! ;)
We are going into the whole 'Divine Identity' part of this now. So, who are you?
You can be a lot of different things to many different people - 'friend', 'brother', 'workmate', a 'random dude on the street', but who are you really?
You can be like Adi Shankaracharya and say "oh that's an easy one, I am Shiva" but then again, Adi Shakaracharya kinda was.
You could say all of those things are Shiva and you'd be right. I could say that Shiva is the most beautiful, deeply spiritual, profoundly esoteric, sacred yet potent, mysterious, understanding, wise, patient, infinitely knowledgeable being/thing I have ever seen, felt or otherwise experienced and I would be right.
I mean, I couldn't even be
half of the things Shiva is...not even a tiny fraction of the characteristics of what I know about Him...which isn't much...like the tip of an iceberg it is.
So when others say that "you are Shiva" or "Shiva is within you" I am like...'woah...hold your horses there, my friend...I wanna hear
Him say that". lol
Aum Namah Shivaya