Renaming your site and changing your domain (URL) are two different things. Your site's name can be found on your browser's tab.
To change your site's name, navigate to Settings, go to General Settings, and next to Storename, add your new name.
If you do change your site's name, make sure your domain matches it so users can find it easily. Read the article "Change Your Site's Domain Name" to set a different URL.
You can also change to a custom domain instead of using Uscreen's domain.
Things are a bit different when considering your apps. If you plan to rebrand or rename your apps, you will need to email email@example.com for more information.