In Shrek the Third, we see the Puppet Master and we know it's him because of the following conversation with him and Prince Charming.
Prince Charming: And you? Your star puppet [Pinocchio] abandons the show to go and find his father.
Puppet Master: I hate that little wooden puppet.
It's unclear what his name is or what version of the character he's based off of, but in the video game, his level is called Stromboli's Workshop.
So is his name Stromboli after the Disney version?