AF Hall of Fallacies

[robvalue]

I'd call that conflation.

It's treating two concepts as if they are the same, and transferring properties between them. In this case, the property that has been "established" for the deistic God is that it exists. They are then treating their specific God as the same thing, so it also exists.

It's also called "bait and switch" for this kind of example, where you swap out one thing for another and hope no one notices.