Oil pumps rarely ever fail and usually last the life of the car or other vehicle that the oil pump is in.
As long as you keep the engine pan full of engine oil then the oil pump should keep lubricated and last a very long time.
It's rare that a vehicles oil pump fails but if the oil pump does go bad then the noise that an oil pump makes is a loud whining or whirring sound while the engine is idling.
If the engines oil pump is making noise then the noise may get louder the faster the engine goes so when you accelerate then the engine oil pump will likely increase in the noise level.