When you open a window in your browser, next to the site url, you see an icon. This icon represents and identifies your site. But when installing Magento, the icon displayed is that of the company Magento Inc.
Technically, this change will not bring any advantages to your store. But it helps in the ergonomics of the site, because it is paying attention to these small details that you become more professional and gain the confidence of the user.
Favicon
fav-icon. It means favorites icon. Because they were initially displayed only when you store the site address to your favorites. But with the evolution of the browsers, soon they were gaining space and being displayed next to the url, and later in the tabs of the navigator.
Syllabic separation: fa-vi-con

Favicon in Browser
Note that all large companies use a custom icon that represents the site. Most sites prefer to use their own miniature logo.
Creating the Icon
To create the icon there is not much mystery. Just ask the webdesigner to create a 16×16 image with .ico format extension.
If you do not have a webdesigner on your team, you can visit the www.favicon.cc site, upload your logo, and automatically generate the icon.

Favicon Preview
You can still view the site itself as favicon will be visible in the browser before you download it.
Other options for generating your icon: Logaster or WebSite Planet.
Changing the store’s favicon
In older versions of Magento, prior to 1.4.2.0 you will not find this option available in the backend of the system. So if you’re using version 1.4.2.0 or higher, navigate to:
System > Configuration > GENERAL > Visual [HTML Header]
In the first option you will find “Favicon Icon“, and the option to select and send your image.

Change Favicon in Backend
Remember that you can send an icon to each store installed, just select the store view from the left menu before making the changes.
Hard-code modification
As I just mentioned, in older versions of Magento it was not possible to make this change through the system. Only the hard-code option remains, meaning it is an option that keeps working if you are oldschool.
Just override the favicon.ico image that is in the skin directory of your template/theme. For example:
skin > frontend > default > default
After you change the image, you need to update your Magento cache, as well as your browser’s cache.
And for anyone who is developing Magento themes, do not forget to include a custom favicon.ico in the template/theme folder you are creating.
Other favicon
You may have already noticed, but the favicon that appears in the frontend of Magento is different from the favicon that appears in the backend.
That is, when you make the change through the system, or in the template files, the favicon image on backend will continue to be the default of Magento Inc.

Backend Favicon
If you want to change this image, simply override the favicon.ico file that is in the directory of your Magento installation in the first directory.
Success!