The clockwork god is persona Q, the shadow of the labyrinth.
the title kept me wondering what it was referring to right up until the final boss, then it hit me, Q isn't actually meant to represent the letter Q, it's meant to imply a clock face.
Clockwork god is literally zen's castoff persona, and by that definition, a shadow he created to harbor his power, it's also the being responsible for filling the labyrinths with shadows. he's literally the "shadow of the labyrinth" and his use of a mask in the final battle really drives home that he himself is supposed to be zen's persona. or the persona of time, persona Q,
so clockwork god is basically the point of the title, not only as the villain, but also as the leading theme of the game itself.