Possibility to update/modify task names, before they're executed, with relevant information such as a Job number and information from the trigger such as the file name. At the moment variables added to the task name aren't further translated.

What would you want to use this information for? When you say Job number do you mean Job ID?

I mean a numeric job id/job number. I need this for our MI reporting where we register every job that is run and its result. I want also add this number to the tasks in order to see the relation between the jobs and their tasks.

If you go to Interface ->Set Columns you are able to show a Job and Task ID which can be added to reports/emails

I assume this is the ID of the job/task and not instance. Do the instances have their unique ID?
Furthermore, we want to create a job manager database where we log all the jobs we process. Is it possible to read the job number from the database and add it to the instances that are processing that particular job?