Final answer:
The variant of panpsychism linked with the idea that shapes and objects have consciousness is related to the double aspect theory, which considers one substance having both a physical and mental aspect, as discussed by Spinoza.
Step-by-step explanation:
The variant of panpsychism that posits not just matter, but also shapes and objects have consciousness does not have a specific name, but can be related to double aspect theory which says there is one substance with two aspects (mind/body). This theory is closely associated with the philosopher Baruch Spinoza.
According to the double aspect theory, everything in the universe has both a physical aspect and a mental aspect, proposing a form of monism instead of dualism. This view suggests that shapes and objects could not only possess physical properties but also mental or psychological properties, integrating consciousness into their very essence. It moves beyond common panpsychism by suggesting an intrinsic duality to all existents within the fabric of reality itself, which includes their forms and structures. This theory would suggest a sort of universal consciousness residing in all things, whether they are traditionally considered living or not.