Bultmann's theory that names were added to Gospels over time — and why it fails

Rudolf Bultmann theorized that names were added to Gospel stories over time as legendary embellishment. If true, later Gospels should have more names than earlier ones. But the opposite is observed: Matthew and Luke (using Mark) tend to drop names from Markan stories, not add new ones. The tendency to add names to anonymous figures is not detectable until the fourth century — hundreds of years after the Gospels were written. This falsifies Bultmann's theory.