For example whether an organism is unicellular or multicellular would be its _.
There is a word 'cellularity', though I don't think that is quite the word I am looking for.
As a sometime cell biologist, I offer that whether an organism is unicellular or multi-cellular is dependent upon its structure. I apologize if this feels overly simple, and there are other words that would suffice; however, it is certainly accurate to state that:
a single-celled organism is and has but one cell, in and around which all the activities of a living thing occur: metabolism, respiration and reproduction being the generally accepted definitions of life
a multi-cellular organism (that is not a colony of single-celled creatures but, rather, one living entity) has a body (structure) consisting of more than one cell, and these cells -- as a whole -- define the organism... and are all (generally) required for all life functions of the organism to take place.
Respectfully, Dr. Jonas Moses
"Cell morphology" describes how it literally looks.