When we bought our sofa bed from Room & Board, we asked for the name of the manufacturer and they told us. We weren't trying to do a direct buy, we just wanted to research the manufacturing process before buying.

You could call and ask for the name of the manufacturer of a specific table, or go into the store and ask.

Also, there's a R&B outlet in Minneapolis, if you're anywhere near there.

Products sold by Room and Board usually can't be bought at other stores, because R*B has exclusive arrangements with their suppliers not to supply other stores. Crate and Barrel and many (any?) other stores large enough to do this also do the same thing.