The only people allowed to address him by that name are the President [Episode #84: "The Hot Line"], his former boss, CONTROL's first chief, Admiral Hargrade [Episode #59: "A Man Called Smart, Part 2" and others] and, mysteriously, KAOS agent Mary "Jack" Armstrong with whom he has an unexplained past. [Episode #15: "Survival of the Fattest".]
He is much more comfortable using the cover name Harold Clark.
There was a character called the Chief in the series Treasury Men in Action, portrayed by Walter Greaza. Thaddeus is probably a spoof of Greaza's character, transposed exactly from the earlier series.