In my admittedly limited testing, I seem to be able to get a script's file name merely by using:

set scriptName to my name

This gives the file name of the script (or the name of the script's window in Script Editor) without the extension. You haven't given many details about what you're doing, though. Your question seems to imply that you are either:

• making multiple copies of the same script with different filenames for different purposes, which seems redundant
• frequently changing the actual filename of your script to produce different effects, which seems odd
• loading external scripts into a script using the load script command, which is sophisticated, but strikes me as something outré enough that you would have mentioned it

Can you give more details about your actual goals?