* Puzzle designer
* Puzzle maker
* Jigsaw puzzle creator
* Jigsaw puzzle artist (if they are particularly creative with the images)
* Puzzle enthusiast (if they are passionate about creating puzzles)
You could also use more general terms like:
* Artist
* Craftsperson
* Inventor
Ultimately, the best term to use will depend on the specific context and the person's role in the puzzle creation process.