How I could get the notebook name having the kernel .json runtime key or OS process ID?

You should be able to find the user fairly easily. If you’re running JupyterHub on a a single shared server with multiple operating system users you can see easily who owns a process using tools such as ps. For something like Docker or Kubernetes you can obtain the contain CPU/memory usage through the platform.

I don’t know whether you can easily from from the PID to the notebook/kernel though, hopefully someone else can help!