How to add pic to website profile

I am not sure if this is possible in WordPress but I hope so. If you look at the tabs when you go to a website you see the website pic/avatar and then next to it on the right you see the name of the website. My question is HOW do I load my avatar to show when my website is loaded? Example: WordPress has a circle with a W in the middle, and google is a square with a G in it. I want a logo for me new site, please help!