Let’s clear this up once and for all. You get a WordPress blog and then notice that other blogs don’t have the Word Press icon next to their URL in their address bar.
First, you have to know what the cute little thing is named. It is called a “favicon” due to it originally showing when you added a site to your favorites in Internet Explorer.*
Second, you need to that WP gave it their own name, Blavatar. If you search for “favicon” in Word Press Help there are instructions on how to add your own: