In the Process Builder, it is possible for one to duplicate existing process under the same package using the option available in the process's properties.
Figure 1: Duplicate Process
That is all that you need to know if you need to merely duplicate a process but if you would like to know more, please continue to read on.
Since the design is made up using XML, we may inspect on what is going on behind the scene.
Figure 2: Duplicated Process as "process1"
Figure 3: Both processes share the same set of participants
Take note that both processes would still use the same of of participants. Modifying the name or removal of participant at any of the processes may affect all other processes that uses the particular participant.
Figure 4: Delete and Remove participant
Remove participant will only remove the swimlane from the particular process. The participant would still exists in the design package.
However, Delete will completely erase such participant from the entire design package. If there's any process that uses the deleted participant, you may see the following in the screenshot.
Figure 5: Deleted participant causing problem to existing processes
Depending on your design requirement, sometimes, you may not want to share the participants across the same processes so that you would have the liberty to rename your participants individually without affect any other processes, you will need to either:-