Who would one hire to make a cabinet door that matches existing cabinets?
Carpenters don't usually do custom cabinetry--it requires a special skillset and some specialized tools. Some do, of course, and if you find a high-caliber handyperson he or she could probably get the job done. 

A better bet is probably a local custom cabinet shop. They'll have the tooling required to match your design, edge profile, etc., and they'll be more likely to have the products on hand to create the wood finish to match your existing. They're also likely to be more expensive than the handyperson due to overhead costs. 

Certainly ask your cabinet seller what they can tell you about finish products. A good cabinet shop won't need it, but it's probably helpful to have anyway. Otherwise just leave one of your doors with the shop while they do your project.