The origin of the unification model for active galactic nuclei (AGN) was the detection of broad hydrogen recombination lines in the optical polarized spectrum of the Seyfert 2 galaxy (Sy2) NGC 1068. Since then, a search for the hidden broad-line region (HBLR) of nearby Sy2s started, but polarized broad lines have only been detected in ~30–40 per cent of the nearby Sy2s observed to date. Here we present new VLT/FORS2 optical spectropolarimetry of a sample of 15 Sy2s, including Compton-thin and Compton-thick sources. The sample includes six galaxies without previously published spectropolarimetry, some of them normally treated as non-hidden BLR (NHBLR) objects in the literature, four classified as NHBLR, and five as HBLR based on previous data. We report ≥4 detections of a HBLR in 11 of these galaxies (73 per cent of the sample) and a tentative detection in NGC 5793, which is Compton-thick according to the analysis of X-ray data performed here. Our results confirm that at least some NHBLRs are misclassified, bringing previous publications reporting differences between HBLR and NHBLR objects into question. We detect broad Hα and Hβ components in polarized light for 10 targets, and just broad Hα for NGC 5793 and NGC 6300, with line widths ranging between 2100 and 9600 km s –1 . High bolometric luminosities and low column densities are associated with higher polarization degrees, but not necessarily with the detection of the scattered broad components.