I've dented the rim on my Shimano WH-RS-10 rear wheel. I found the tech doc pdf. I've had wheels rebuilt before but always with rims that were available to consumers. I can't find any place that sells the Shimano rim, nipples, or spokes to rebuild this wheel. I know I can get close matches from other companies, but I'm looking for identical components to match the good front wheel I have. Does Shimano actually provide these components for sale? Would this be something my LBS could order?
Yes, you can order replacement parts from an LBS who is, or has access to a Shimano distributor.
You are unlikely to find that rim or those spokes in stock, because they are unique to the wheel, and it is not cost effective for a shop to keep them on hand given the relatively small chance that someone will need them.
Ordering them, though, should be straightforward, and cost less than 200 dollars.