An apparatus and process for hydrodesulfurizing hydroprocessed naphtha from an overhead stream of a product fractionation column and/or from an overhead stream of a product stripping column in which an overhead stream may be condensed and fed to a post treat hydrodesulfurization reactor. Hydrogen may be supplied from an upstream separator for separating the hydroprocessed stream. Accordingly, naphtha may be hydrodesulfurized within the hydroprocessing recovery unit.