The destroyer name records a shift from defence to attack

How did the torpedo-boat destroyer become the modern destroyer?

It evolved naturally from torpedo boats to defensive torpedo-boat destroyers and then to torpedo-armed ships simply called destroyers.

The early vessel was a torpedo-boat destroyer built to protect larger ships from torpedo craft. Designers then gave the defensive vessel torpedoes of its own, allowing it to attack as well as screen. As the type grew into an independent combatant, the longer compound name became unnecessary. The shortened word destroyer therefore preserves the lineage of a ship whose original target was another small torpedo vessel.