This will update the site name that appears across your Moodle site.
Step 1. Login as an Administrator and Select Site Administration.
Step 2. Select the Site Administration tab (this is often the default landing page after selecting the default landing page button).
Step 3. Find the Front Page section.
Step 4. Select Front Page Settings link
Step 5. Update the Full Site Name field. Which will update the site name which appears across the Moodle site.
Step 6. Scroll to the bottom of the page and select Save Changes to apply the change.