Where did the idea that Frankenstein is the name of the monster come from? I know that the monster is addressed as Frankenstein in several spin-off movies, but after doing some primary research, I can't find where this idea came from.
Actually, it started very early on and probably wasn't inspired by anything in particular. Probably it was created of either laziness ("Frankenstein's monster" is so long) or ignorance ("Dracula" is both the name of the book and the monster).
As I wrote elsewhere, using "Frankenstein" to refer to Frankenstein’s monster dates back to at least 1838, only 20 years after the book was published according to the OED:
They [sc. mules] really seem like Frankensteins of the animal creation.
Murray's Handbook Sicily
Here's another example I found from only a year later, in 1839:
Two gigantic empires—the Frankensteins of our own creation, which will soon turn upon the author of their being—are shooting...
The London Quarterly Review
It seems really unlikely that there's any single path, and the monster is "a Frankenstein" in at least some of the same ways that a Model T. is "a Ford" or Guernica is "a Picasso." But James Whale is also obviously a key tributary of the drifting reference.
James Whale's 1931 movie with Boris Karloff (the seminal visual depiction of the monster) totally centers the monster in a movie called "Frankenstein." Moreover, many (if not all) of the posters for the film have the text "Frankenstein" superimposed on Karloff's giant forehead.
James Whale made a 1935 movie that not only compounds, but trades on the ambiguious reference, being called "The Bride of Frankenstein." The bride is of course a bride for the Monster, conceived by the mad scientist Frankenstein (though not the same Frankenstein as made the first monster!)
The popular recognition of Victor Frankenstein's Creature as simply "Frankenstein" started with the films; since more people were familiar with the films, popular culture began to acknowledge the movie portrayal of the Creature more than the literary portrayal.
See "How Frankenstein’s monster has shuffled through movies and comics" by Rosalind Early-Wustl on Futurity.org (30 October 2017).
From the above link you can see how the Creature has progressed through film; this progression seems to suggest my conjecture.