The study of gamma-ray blazars is usually hindered due to the lack of information on their redshifts and on their low-energy photon fields. This information is key to understand the effect on the gamma-ray absorption due to either extragalactic background light and/or intrinsic absorption and emission processes. All this information has also an impact on the determination of the location of the emitting region within the relativistic jets. In this work, a new optical spectroscopic characterization is presented for three gamma-ray blazars: S4 0954+65, TXS 1515-273, and RX J0812.0+0237. For all the three targets, the redshift determination is successful, and for the first time in the case of TXS 1515-273 and RX J0812.0+0237. Their classification as BL Lac type is confirmed based on these new optical spectra. For S4 0954+65 (z = 0.3694 ± 0.0011), an estimation on the disc, broad-line region, and torus luminosities is performed based on the observed optical emission lines. The results from this study are compatible with the nature of S4 0954+65 as a transitional blazar. In the case of TXS 1515-273 (z = 0.1281 ± 0.0004), although its optical spectrum is dominated by the continuum emission from the jet, applying the pPXF technique, the stellar population can be unveiled and is compatible with an old and metallic population. It is also the case of RX J0812.0+0237 (z = 0.1721 ± 0.0002). Moreover, this work confirms that the optical spectrum from RX J0812.0+0237 is compatible with an extreme blazar classification.