This request has come up before but was closed without comment.
GitHub provides a simple context parameter for this exact purpose, it just needs to be customized.
Running the same job multiple times (with different parameters) is a very common pattern for a large codebase, and seems like an important feature for a CI service to provide.
It could be as simple as allowing jobs to have friendly names, which can be parameterized (e.g. using environment variables), and that is the title reported to the GitHub status API. It would be useful to have this friendly name show up in other places of the UI as well.