After browsing through the VI Logger User Manual, it looks like the triggering that you are hoping to accomplish is possible. However, incrementing the filename for the next logging event is not going to be possible. VI Logger does exactly what its name tells - logs data. I don't think the automation that you are hoping to accomplish is possible.
For help with setting up your application, if you do choose to stay with VI Logger, make sure to chek out the
Getting Started with VI Logger Manual.
Best of luck.
Jared A