What is this style of cupboard door called?
While the "flush" or "integrated handle" style door is common, it's likely that this particular design with this particular molding profile is proprietary. They were probably cheap to purchase initially due to economy of scale, but they may no longer be in production. 

You may be better off refinishing the wood (sand, stain, seal), and if necessary reapply laminate to the face. Creating a new identical door would be an exercise in detail work.