The panel phone with a rotary dial is Western Electric model 750, and the Touch-Tone version is model 2750. There were also multi-line and speakerphone versions available.
I'm looking for a WE model 2832 or 2833 multi-line set with the woodgrain faceplate. I have a Comdial model 2830 10 button set that I plan to hook up to single line service.