How to set an icon when you drag an url from out the website, to the Desktop

I am trying to create a shortcut to connect to a game on my website. Now that works, but now i want to make an shortcut to the game with icon, that people can drag to the desktop.

It already works to drag it, but it needs to have 2 changes: 1. The right icon (Now it's a Firefox icon(dragged from out Firefox page)) 2. The right name

Can somebody help me with this?

Maybe there is also a better way to do this, if someone no let me know.