How to let Arduino know which software is open on my PC?

Is there any way to let Arduino which software/application is open on my PC?

Not directly. You would need an agent application running on the PC.

What's the purpose?

I guess you wrote several programs on the PC to connect to the Arduino and the Arduino should know to which of these applications it's talking to. Just tell it to the Arduino within the serial protocol. You may even adapt the protocol after that to the specific needs of that application on the PC.

I always have my programs announce who they are. They print a Hello message that gives the program name, path, version, revision etc. After this I delay 5 seconds incase I have a serial freeze, this allows me to recover easily. Many times I will close the IDE and later connect back, that causes it to reset and display the Hello message.