Call it strong variationism or strong randomness or strongly random variationism (none of these sound quite right... this is a work in progress). It makes a strong claim about the role of random variation in generating new species. It takes for granted Darwin's understanding of the role of natural selection, as that is not really where the controversy lies. And it allows one to separate the role of variation from controversies about Darwin's opinion regarding divine providence, Lamarkianism (that is, it would seem, on the basis of The Descent of Man , that Darwin himself was willing to attribute a role to use/disuse, now discredited source of variation), racism, eugenics, etc. And it allows us to contrast that with weaker roles that might be given to random variation, again without any unneeded historical baggage.
Commentary and discussion regarding science, faith and culture by Leo White