Jenkins "Git Branches" column showing parameter name instead of actual used branch name

Question

I am setting up a pipeline using pipeline script from SCM. As the branch specifier I use a build parameter.

The specifier is resolved correctly during the lightweight checkout and the regular checkout but in the job overview its showing only the parameter name and not the branch name used for the last build:

This is how I set up the job and its parameter (which is working fine for the script):

So I am wondering if there is any code i can call in the script itself, in order to set the actual used branch name displayed in the job overview.

I tried scm.branches.first().setName("my-branch-name"). This will actually change the branch specifier in the job configuration, so it's not what I am looking for.