Final answer:
The component that protects the starter motor from damage if the ignition switch is held in the start position after the engine starts is called the starter motor relay or the starter solenoid.
Step-by-step explanation:
The component that protects the starter motor from damage if the ignition switch is held in the start position after the engine starts is called the starter motor relay or the starter solenoid. This device is an electromagnetic switch that engages and disengages the starter motor with the engine flywheel. When the ignition switch is turned to the start position, the starter solenoid receives a current signal and activates the starter motor, which starts the engine. Once the engine is running, the feedback from the engine's rotation causes the solenoid to disengage the starter motor, preventing it from damaging itself or the engine.