Name a few songs that you consider the "signature song" of a particular band or solo artist. This is just for fun, and from your own standpoint, but give it some thought.
One way to look at it would be, if the band were interviewed on a talk show, what song would be used as they walked onto the stage? "Hail to the Chief" is for the President, so what song would be used to introduce or accompany .... ? (you name it)
There's bound to be more than one for many artists, as their catalogs are enormous, so this is just your quick take.
If you want to stick your neck out, in your estimation, do the Beatles have a signature song? At this stage of his career, how would you even select a song for Paul McCartney? Beatles, Wings, solo ...?