Site Name and Site Slogan
The "site slogan" is the text under your site name. On this site, for example, our site name is "Drupal at Cal Poly" while our site slogan is "Cal Poly's Content Management System".
To change the text of your site name or site slogan, navigate to Configuration -> Site Information. There is a plain text field you can edit for both the name and slogan. Make sure to scroll down and click Save to commit your changes.
Changing the Links for the Site Name or Site Slogan
The site name will always link to your website's homepage. However, you can change the path of your homepage on this same Site Information page. It is defined under "Default front page".
Your site slogan is not a link by default, but it can be made into a link if you wish. To modify your site slogan link, click on Appearance, then Settings (for the Cal Poly Standard Responsive theme). The URL your site slogan points to is defined under Site Slogan Link (optional). It may be left blank if you do not want it to be a link.