A process has initiated with data, process display and node display expressions

@srinivasak 'I was under impression, process and task display names should also change since it is depends on process variable data' - here goes the explanation as per my experience:
1. Process name: Process name itself is identified by a variable called pp!name, which is one of the process properties. So here you are copying the value from one variable (A pv which you have created for saving the value and thereby used for saving value into Process Name.) to Process Name (pp!name). So here you can't observe a change in Process Name if you make a change in the Process Variable which is used for copying the value to Process Name. Simply speaking, neither there is any connection between the PV which you created for saving the value into 'Process Name' and the process property 'Process Name' (which is identified by pp!name) nor there is a pass by reference kind of mechanism.
2. Task Display Name: I couldn't make a comment at this point, but out of my experience, I have seen that once if a task has been initiated with the process variable in its Task Display Name, there won't be change in the title (the name which we see in the 'Tasks' list) after modification in the value of PV until the next instance of task is started. A possible solution could be storing the value in database and making a query in the 'Task Display Name' if you feel that Task Display Name is dynamic in nature.

@srinivasak 'I was under impression, process and task display names should also change since it is depends on process variable data' - here goes the explanation as per my experience:
1. Process name: Process name itself is identified by a variable called pp!name, which is one of the process properties. So here you are copying the value from one variable (A pv which you have created for saving the value and thereby used for saving value into Process Name.) to Process Name (pp!name). So here you can't observe a change in Process Name if you make a change in the Process Variable which is used for copying the value to Process Name. Simply speaking, neither there is any connection between the PV which you created for saving the value into 'Process Name' and the process property 'Process Name' (which is identified by pp!name) nor there is a pass by reference kind of mechanism.
2. Task Display Name: I couldn't make a comment at this point, but out of my experience, I have seen that once if a task has been initiated with the process variable in its Task Display Name, there won't be change in the title (the name which we see in the 'Tasks' list) after modification in the value of PV until the next instance of task is started. A possible solution could be storing the value in database and making a query in the 'Task Display Name' if you feel that Task Display Name is dynamic in nature.