They will probably only know Gillette and some no-name they tried once and hated. If they were to see Dorco on Amazon most consumers would put this into the latter category. On the other hand, DSC has good enough marketing to convince many consumers that DSC are in the Gillette category for a fraction of the price.
Personal care products are frequently 20% product, 80% marketing. There are store brands for practically every product in this category, yet name brands do okay.