A naïve fix will regress JENKINS-36574.

Then maybe it makes sense to add the ability to configure the context from the pipeline?

More likely from the multibranch / organization folder. Fine so long as the default remains a fixed string (per job type, at any rate), and the inline help clearly explains why you might run into trouble customizing that.

When you run multiple Jenkins job per Github PR you currently end up with having several "continuous-integration/jenkins/" status messages.
It's unclear which status refers to which CI job (build, test, etc).

Alternatively being able to disable posting the status to github from the plugin at all would help.
Then I could post the status myself with a script with the information I want.
When I currently do this, I end up with multiple status messages for the same job run in github.

This is really annoying. the build commit status will be overwritten if you have more than 1 jobs triggered by a single commit because they are using the same context label. job name should be used for the context.

Is there a way to customize the context name via the pipeline api or jenkins api ?

Do not do this. There was an issue specifically requesting that the context string not include details like a job name, and that was fixed. The reason is that GitHub has features whereby you can control various workflows by specifying approved status context strings, and they need to be an exact match.

quote from a comment of the closed PR.