The origin of the unification model for 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% 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, and four Sy2s classified as NHBLR based on previous data. We report >4sigma detections of a HBLR in 11 of these galaxies (73% of the sample). Our results confirm that at least some NHBLRs were misclassified, bringing previous publications reporting differences between HBLR and NHBLR objects into question. We detect broad Ha and Hb components in polarized light for 9 targets, and just broad Ha for the other two. We do not find any correlation between the properties of the polarized spectra and the column densities measured from the X-rays or torus inclination, but a larger sample is required to confirm this.