An elephant head on a human torso was a right-sizing intervention. Elephants, lose evolutionary advantage despite bigger brains - burly physique being harder to feed and multiply. Bringing similar neural capacity to humans was not natural - it was a divine intervention.

There is a mythical narrative to etch this idea in public discourse :

Ma Parvati, wife of Siva, created a humanoid from her body scrub. It worked but it wasn't context aware. It was programmed to do only one task - protect its mother !

When Siva returned home the humanoid wouldn't let him in. Siva - the epitome of conscious experience - had to engineer context awareness in him. Metaphorically, he planted an Elephant head on young humanoid. Being the mind child of Siva, he imbibed divine intelligence and soon became leader of Siva's network of followers (Ganas). Thus, the name Ganesa.