It seems to me that the Creator must also be the ultimate Designer. Nevertheless, the notion may also be acceptable to non-monotheistic faiths.
The thing that strikes me as odd about "Designer" is this line: "To cause completely something to exist is not to produce a change in something, is not to work on or with some existing material." Insofar as Intelligent Design treats its designer as one who works using existing material, it only describes a semi-Platonic demiurge.
I've forgotten whether Behe et al. think God created ex nihilo a new gene sequence or cellular structure for a given creature or simply directly tweaked the creature's pre-existing structures, but the very awkwardness of either option on both theological and scientific grounds makes me wary of their school of thought, no matter how much I like how it has shaken men from their slumbers.