The other way the jobname can be updated is in a SPLIT component there is an option to 'Append Rule Name to Job Name'. So you could set the Rule Names to be what you want appended to the 'jobname' based on the branch or split.
So I think you are asking to update or change the 'jobname' based on different branches in the workflow. So yes, you can change the 'jobname' but the only way to do that is to use the SAVE component. When you save the file you can control the filename. However, you cannot change the jobname in a workflow. In some cases you might save the file with an updated jobname and its save location could be a hotfolder for another FreeFlow Core workflow that then sends it to the printer etc. with the updated 'jobname'
Is it possible to set parameters like quantity or sides imaged within the workflow itself, provided that there is no job ticket and no MAX setup?