Can I have two separated serial monitor for the same arduino board connected to PC?
If you want to have two Serial Monitors, start the IDE twice. Use your desktop shortcut or start menu entry to start the second instance of the IDE. In the second instance you can select a different port. It will not work for Upload of course, but when you open the Serial Monitor, it will work at the selected port.

Other option is to use some terminal program to see the output of the com port.

The other answers cover the fact that you need an USB to TTL Serial adapter to connect to USB and in sketch SoftwareSerial as your second serial interface or use some board with two or more hardware serial ports like the Mega on the picture.