If there was any "symbol" of The Church of Jesus Christ of Latter-day Saints it would be the savior Jesus Christ since he is the head of the Church and our Lord and Savior. He is the perfect example of what we as Latter-Day Saints do our best to emulate on a daily basis.  
 
We have no cross or fish to wear around our necks or top our chapels with. The only LDS building you will see with a symbol on top of it is our Temples, they are crowned with a figure of the Angel Moroni pointing his trumpet towards the Eastern Horizon which is the direction the Lord will come from when he returns again to usher in the Millennium.  
 
When I was in the US Army I saw the only religious medallion for LDS ever, it is a oval shaped stamped coin with the inscription " I am a Member of the Church of Jesus Christ of Latter-day Saints" with a image of the Salt Lake City Temple. The back had information about contacting Salt Lake for any inquiries about religious rites to be performed for LDS Service Members.  
 
I see the same token in some LDS Stores though I have only seen them warn by US Military personnel to help the chaplains identify there faith of fallen service members .

I would say one of the best ways you can see the symbol of the LDS church is by the way the people live and the standards of the church... 
 
No alcohol, No tea, No coffee... how they dress act... its not in the worlds standards how we live, i like how paul put it in. 1 tim 4:12.. "Let no man adespise thy youth; but be thou an example of the believers, in word, in cconversation, in charity, in spirit, in faith, in purity." 
 
well hope this helped!