There isn't a way to remove your site name (sitewide settings > general > site name) from within the dashboard. If you try to remove your site name it goes to the word concrete5 instead.
You will need to do a bit of PHP coding, but it is fairly easy to do this even without much PHP experience.
you need to edit your header.php file which is usually in /themes/mytheme or /themes/mytheme/elements
You will need to edit your header.php - make a backup of this file before changing it (just in case!)
your header.php should have code that looks something like this:
if you are using the default (plain yogurt) theme this would be at line 30.
Remove this block of code and now your site name will be removed from your site.
Not too bad, right?