I believe your question is about creating a “favicon”. This is a small image that is served up by your site and appears on each browser tab you may have opened.
The WordPress Codex lists a convenient step-by-step on creating a favicon.
http://codex.wordpress.org/Creating_a_Favicon
Creating a Favicon
A favicon can be created using any graphics/image editing software, such as GIMP, that allows the saving of .ico files. There are also online services that will allow you to create a favicon for free.
The image should be clear and is usually designed to match your blog’s image and/or content, a big task for something so small.
To prepare the image to be saved as favicon.ico:
By cropping or adding space around the image, make the image square.
Resize the image to 16 x 16 pixels.
Save the file as favicon.ico.
If you’re using an online service to create your favicon, such as Faviconer.com (creates 24bit favicon.ico with a transparent background, favicon.co.uk or Dynamic Drive, follow the instructions provided by the site and then download the favicon.ico image to your computer.
Installing a Favicon in WordPress
If there is already an old favicon.ico file in your current theme’s main folder, delete it using FTP Clients.
With an FTP Client, upload the new favicon.ico file into your current theme’s main folder.
Upload another copy of your favicon.ico file to the main directory of your site (ie. http://example.com/favicon.ico). This will display the favicon in your subscribers’ feedreaders.
In order for your favicon to show up in some older browsers, you will need to edit your page header. Remember, the best way to edit your theme’s files is via a Child Theme. For the purpose of the following instructions you will need to create a copy of your parent theme’s header.php file in your child theme.
Go to your WordPress Administration Panel.
Click on Appearance.
Click on Theme Editor.
Select the file called Header or header.php to edit the file.
Search for the line of code that begins with . Overwrite it, if it exists, or add the following code below the HTML tag.
/favicon.ico” />
Save the changes.