The multi-frequency sedentary survey is a flux-limited, statistically well-defined sample of highly X-ray dominated (i.e., with a very high X-ray to radio flux ratio) BL Lacertae objects, which includes 150 sources. In this paper, the third of the series, we report the results of a dedicated optical spectroscopy campaign that, together with results from other independent optical follow-up programs, led to the spectroscopic identification of all sources in the sample. We carried out a systematic spectroscopic campaign for the observation of all unidentified objects of the sample using the ESO 3.6m, the KPNO 4m, and the TNG optical telescopes.