Another name would be simply: air pump. Stop looking on computer, and go to a good auto parts store. They'll probably have what you need.
I disagree with the mechanic. He's just trying to rip you off. You don't need this part to start your car AT ALL. Go somewhere else that is reputable, and NEVER go back to that mechanic again! (Unless he is your husband, then cut him a little slack).
NOTE: Dealerships are notorious for the high prices they charge for auto parts. This is because they use new, original parts, and also because they want the money. Only use them in as a last resort. Use an auto parts store instead. Rebuilt air pumps are as good as new, and cost half the price, or perhaps even less than that.
PS: always take a man with you when you go to a mechanic. Let HIM do the talking. Or just let him go alone. Mechanics are notorious for ripping off WOMEN. Keep your mouth zipped, and act like you know nothing. Let the MEN talk.