Yes, you can do this in My Screen Recorder. You need to change the File save options.
Follow these instructions:
Click on Settings icon on tool bar and go to 'File Save' tab.
[image: Filesave.png]
Change the default file name and select either 'Append date and time at the end of the file name' or 'Append sequence number, if file with same name already present'.
Now, when you perform number of recordings date and time or a sequence number will be appended to file name.