The name of Mr. Peabody's time machine is WABAC (pronounced "Way-back"). It resembles a typical computer of the time, which could take up an entire room of the office building. Such computers often had names like ENIAC or UNIVAC, with AC standing for Automatic Computer. Show director Gerard Baldwin stated that WABAC was intended to parody UNIVAC specifically. (In Mr. Peabody & Sherman (2014), WABAC's full name was retconned as Wavelength Acceleration Bi-directional Asynchronous Controller.)
Paul Frees was the most frequent voice actor for the historical figures in this series. Within the Bullwinkleverse, Frees also provided the voices for Boris Badenov in The Bullwinkle Show (1959) and Inspector Fenwick in The Dudley Do-Right Show (1969), and numerous incidental characters in the series.
Mr. Peabody's full name is Hector James Peabody. Sherman is Peabody's adopted son, so his full name is probably Sherman Peabody.
There are three different opening titles sequences for Peabody shorts. One is the parade, where Peabody and Sherman ride in a Roman Empire chariot behind elephants, soldiers, and a litter with a beautiful woman relaxing on it. Another is Sherman walking through a museum which displays pictures of Peabody throughout history. Rounding out the list is the one with Peabody and Sherman riding a succession of vehicles into the past.