The problem with that is that a group as vague and big and diverse as “the left” will never be able to force a descriptor on itself - mostly because there are people on what you can conceivably call “the left” hate each other and do not want to associate at all. Rather, any descriptor like this will come from outsiders, typically starting out as a derogatory label that combines people based on who the label-giver hates, rather than on any real similarities between the people in the group - both “left” and “right” started out like this!

Maybe someone (even you) can start some kind of an organization within the leftist movement called “pro-human party”, and see how that plays out.