See https://docs.sonarqube.org/display/SONAR/Documentation for current functionality
You can set your own "home" logo in Administration > General > Look & Feel. Simply provide an image URL and width. Ideally, the width will scale the height to 30 pixels.
Gravatar support is enabled by default, using gravatar.com. You can configure a different server or disable the feature altogether. When enabled, gravatars show up next to most uses of the user name: