They call it an avatar. As long as you have something to replace it with, it's pretty easy. Roll your mouse over to home in the upper right. Click account, click profile. Pick a file from your computer. Probably save changes or something and then it might take up to a day before it shows up.
How to change icon next to handle?

you have a dimond, i have a queen crown
not pic avatar
You have a platinum membership here, that is the icon to show that you are premium member at that level. baddogno is a diamond member, therefore the diamond icon.
See: http://www.chess.com/membership?c=icon
I have a queen icon that i do not want,but i dont know where to change or how. If any one knows how ,would be helpful.