Google can display your favicon next to your search result snippet in the search results. Google's John Mueller stated that the favicon used to identify your website is only displayed on your home page.

"Last I looked, I guess we merely picked up the homepage favicon," John tweeted.

I suppose that if you use various favicons on various sections of your website, Google will ignore the other pages and only use the favicon from the home page as the favicon it displays in the search results. However, I don't recall ever seeing a website use various favicons for each page; have you?

Here are those tweets: