The first step is you go to Dashboard.
Next you click on Settings. Select General.
Now you should see the page called General Settings.
Then you replace your old blog name with a new name in Site Title.
And you click Save Changes.
Now you should be able to see your new Blog Name or Site Title on your blog.
But many of you have this problem where your Old Blog Name/Site Title Still Shows On Title Bar.
Note: It is all because you used the All In One SEO plugin. To get your new blog name of site title appearing or showing on the title bar, this is what you do:
2. Click on All In One SEO.
3. Look for Home Title:
4. Replace it with your new blog name.
5. Click Update Options.
*Update: The above tip is NOT applicable anymore. With the latest WordPress update, you cannot find "All In One SEO" under Settings. It is now listed above "Posts".
Go to "ALL In One SEO", then click on "General Settings". Scroll down to "Home Page Settings".
Make the chances there. Then scroll all the way down and click on "Update Options" button.