The nickname "Mad Dog" is generally reserved for serial killers and psychopaths. Gen. James Mattis earned his nickname during the 2004 Fallujah campaign when he dropped white phosphorus munitions on civilians in violation of international law. He is said to hate the moniker.
Some other examples of men called Mad Dog.
Adm. Zinovy Rozhestvensky
The Japanese knew he was coming and were prepared. On reaching the Tsushima Strait between Korea and the Japanese island of Honshu the Russian fleet saw its path blocked by the Japanese fleet in a crossing the T formation.
The wise and prudent thing to do would be for the Russians to withdraw and avoid battle, which were Adm. Rozhestvensky's orders. But the admiral was insulted that the Japanese Navy was blocking him and in his anger blindly charged the battle line.
The Japanese bombarded the Russian fleet with broadside after broadside while the Russians could only respond with far smaller bow guns. Two-thirds of the Russian fleet was sunk and the rest surrendered.
Vincent "Mad Dog" Coll
Coll died in 1932. Schultz had put a hit out on him and he was submachine gunned down while using a telephone in a Bronx drug store.
Marion Pruett gave the name to himself. In 1979, Pruett was put in witness protection after testifying against another man for a murder Pruett had committed. In 1981 while under federal protection, he killed his common-law wife by beating her to death with a ballpeen hammer. In the following week he shot and killed four other people across two states.
He claimed to have killed others and offered to revel the location of a Florida victim if he got a paid interview with Geraldo Rivera.
More About Mattis
I have not found a single example of a sane, rational person who has been given the nickname "Mad Dog." Just saying, probably not someone you want in charge of a two million person military.