Here is an example of what I am trying to do:
In case someone got here from search engine, the accepted answer will work only if the script is in server root directory, as PHP_SELF is filename with path relative to the server root. So the universal solution is
basename($_SERVER['PHP_SELF'])
Also keep in mind, that this returns the top script, for example if you have a script and include a file, and then in included file include another file and try this, you will get the name of the first script, not the second.