I don't think that level of customisation is provided. However, I can suggest some workarounds:

• REST API: Create a job on the fly with desired name within ADF and trigger it using REST API in Web activity. This way you can track job completion status and decide what action to take if the job run was success or failure.
• File trigger: Drop a file at a location using ADF, and set file arrival trigger in Databricks job. This will ensure that you're running the same job in Databricks.

Hope this helps.