The thingy where you click an icon to do start an application is called a "launcher".
If this is just for you, then you right-click anywhere on the desktop and select "create a launcher" and fill out the dialog. (Gnome) usually, you get the launcher to run a script file which, in turn, runs your executable.
If you want all this automagically installed on the desktop of whoever types "make install", then this is trickier.
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