The GitHub Checks app only shows the name 'Bitrise' and the status of the build for the CI check. There's no way to instantly see which Workflows were running, for example.
Unfortunately, GitHub Checks does not support custom names. You can, however, use the GitHub Status Step: this Step updates the commit status on a GitHub repository with a build's status. It also allows you to add custom names to your status updates.
However, as the Step of course runs during the build, it can't be used to report on events that occurred before or after the build. For example, it won't report that a build is on hold or that it has been aborted.