Perhaps a little peripheral to your question, but it appears that the Romans did incorporate Yahweh into their magic. This is an example of a magical gem with an anguipede on it. He is surrounded by the letters ΙΑΩ which are the Greek equivalent to the tetragrammaton. There are a ton of other examples as well either with these letters or with other references to Judaism such as the sacrifice of Isaac and inscriptions written in fake Hebrew.

The Greeks had a kind of omnivorous view of magic, along the lines of "hey if it worked for someone it might work for me." They incorporated symbols from a number of different religions that we might consider distinct.

And the exchange didn't just go one way! There are early Christian amulets with Greek magic symbols on them and books of Jewish magic that invoke pagan gods.