Yes. From the Widget page you can set your primary and secondary colours, the launcher position (bottom-left or bottom-right), the panel title and greeting, and your logos.
Because the widget reads its configuration at runtime, changes reach your site without redeploying anything. You may need a hard refresh to clear your browser's cached copy of the script.
Custom logos and removing HelpShelf branding are available on paid plans. See Customizing the widget.