is there a way to find out who a person is by a picture alone?

You can download the picture or put it onto your computer. Then go to google.com page. Select "Images" and then drag and drop the image into the google search window. If that person's picture is somewhere on the internet with their name attached to it, then it will pop up. If not, oh well. You tried.

Possible, if it's a publicly known figure, then you can just run reverse image search on Google, or any number of other sites.