This type of ship was devised to counter vessels called torpedo boats, & the name originally followed "torpedo boat"
The British called these countering ships 'Torpedo Boat Destroyers', a 
name... [DOC] [TLE] Destroyer [PAR] Before World War II destroyers were light vessels without the endurance for ... 
and called torpedo boats, and these had developed by the 1880's into little ships 
of 50-100 ... (The anti-torpedo boat origin of this type of ship is retained in its 
name in ...