I am not a scientist, let alone a biologist. I am just a long-time armchair observer of Creationism.
However the word “Darwinism” is just a naming convention, rather than some erudite scientific hypothesis. It is therefore a rhetorical convention that should be judged on whether it aids or impedes understanding and so, I think, a matter on which a layman can offer an opinion.
“Darwinism” would seem to be a bit of an anomaly within scientific naming conventions. The normal practice seems to be to apply the scientist’s name as an adjective to the field in which they are working. Thus we have Newtonian Mechanics and Mendelian Genetics, rather than Newtonism and Mendelism. This convention even applies to work that has drifted to the fringes of science, such as Freudian Psychoanalysis or Jungian Psychology. This convention, I think, is useful in that it positions the scientist’s work as part of their field, rather than rhetorically divorcing it from that field. Using the term “Darwinian Evolution” (particularly when one is emphasising Natural Selection, or distinguishing from earlier conceptions of evolution, such as Lamarckian evolution) would fit with this convention. The use of “isms” on the other hand tends to be more conventional within the field of philosophy: Monism, Dualism, Marxism, and (coming perhaps closest to Darwin) Vitalism. I’m not sure that “Darwinian Evolution”/“Darwinism” is a good fit amongst this company.
I also think that terming this “Darwinism” tends to obscure the contribution of all the evolutionary biologists who have worked since Darwin’s time. Darwin’s work may be the substantial root system of the tree (figuratively speaking), but it is not the entire tree. Using the convention “Darwinian Evolution” implicitly acknowledges that there is more to evolution than Darwin.
This conflation between Darwin and the full corpus of evolutionary work can serve a darker rhetorical purpose. It could be said, without much in the way of exaggeration, that Creationism is simply apologetics justifying a restrictive (YEC) or slightly looser (OEC) reading of the Book of Genesis. Calling Evolution “Darwinism” makes it easier to make a false equivalence – that “Darwinism” is just apologetics justifying On the Origin of Species/the ‘Book of Darwin’, rather than the reality that it is a fecund and ever-increasing body of research. Along similar lines, the ‘just a theory’ canard can be taken a step further, to ‘just Darwin’s theory’ – that “Darwinism” is simply an archaic 19th century holdover, with little relevance to the 21st century. None of this might be said explicitly, but I often feel I detect an implicit undertone of this in creationist rhetoric.
As I said in the beginning, I am not a scientist, so do not have the hubris to tell scientists, who have worked for decades in fields, how they must label them. But words have power: used wisely, to illuminate; used unwisely, to confuse; and used maliciously, to deceive. They should therefore be used with consideration and care.