Application's Status/Script's Name

Question

1st: How do you find out if an app is running? You can see where I don't have it in the top comment, and why in the bottom one.
2nd: Is it possible to change the name of this script application while running itself, this would be at the bottom near changing the property valswitch.
Thanks in advance
Script:
property valswitch : "Dragging"
tell application "System Preferences"
set valpane to current pane --Is it running, if so record pane
activate
reveal pane "com.apple.preference.trackpad"
end tell
tell application "System Events"
tell application process "System Preferences"
tell window "Trackpad"
tell group 1
tell pop up button 3
click
tell menu 1
UI elements
click menu item valswitch
end tell
end tell
end tell
end tell
end tell
end tell
tell application "System Preferences" --If wasn't running before then quit, else go back to pane
if valactive is true then
reveal valpane
else
quit
end if
end tell
if valswitch is "Dragging" then
set valswitch to "Swipe to Navigate"
else
set valswitch to "Dragging"
end if

Answer 1

How do you find out if an app is running?
Ask System Events:
tell application "System Events"
  set isRunning to (name of every application process contains "MyApp")
end tell
Is it possible to change the name of this script application while running itself,
Sure:
tell application "Finder" to set name of (path to me) to "New Name.app"
(don't run this in AppleScript Editor, though, since 'path to me' may return the path to AppleScript Editor and not your script.