Symptoms
The client built a process and deployed it. Later down the line, they renamed a process to get in inline with their naming convention standards. When the start a process now, it gets started successfully, but they see an error in the log files stating "ProcNotFound" for the old process name.
Diagnoses
I was able to reproduce the issue by creating a process, deploying it, renaming it and deploying it again. If you go look in workspace, you will now see 2 processes under the same solution. When you enter a new item in the SP2013 list, 2 process instances will get started. If you delete the old process instance and add a new list item to the list, it will start just the "new" process, but you will see a "ProcNotFound" error for the "old process".
This is because the SharePoint.Integration tables gets another entry when you deploy a re-named process, but those entries does not get deleted when you delete the process from workspace. Because of this, the "old" (Renamed...) process gets started as well with the SP event receivers.
Resolution
I sent the ticket to the LABS support team for investigations. The engineer working the ticket, logged something for us in TFS. If a process gets deleted from workspace, it will perfom the needed cleanup in the SharePoint.Integration tables and the "old" process should not get started again.
As a workaround, I suggested that the client rename the process back to what it was called in the beginning. They can then remove the start options (OnItemAdded, OnUpdate etc etc.) from the process start rules and deploy the process again. (Keep "Manual".) then you can rename the process again, add the start rules and deploy the process. You will have the extra entry in the SharePoint.Integration tables, but because the "old" process can now only be started manually, it will not fire when adding a new item to the list.