Technically it doesn't matter at all, but as a reminder for yourself that a file is a script it is absolutely helpful.
You will need to make the file executable by means of caja (properties) or the command chmod a+x
By the way, although this script of mine does work for anyone who wants to keep 'arctica-greeter', it might be better to replace the lightdm-greeter 'arctica' for 'slickgreeter' which will give you the official 'loginscreen' customizing options.
This link shows you how to do that (including settings):
Replace arctica-greeter back to slick-greeter on 20.10 for better compatibilty with other desktop environments