DC9-80 entered service in 1980, as a stretched DC9-50, 14'3" longer, 25% larger wing area, and, of course, slightly more powerful engines. The Super MD-80 name came along in 1983 as, basically, a marketing ploy. If connected to the Douglas - McDonnell merger, it took a while. The merger happened in 1967.
Up through the MD-88, they all were certified by the FAA as DC-9-whatever-the-number.