Clearly, it's more than just a screwdriver. It could have been called an alien Swiss army knife, or an alien multipurpose tool. Why, then, is it just called a sonic screwdriver?
It's called the sonic screwdriver because originally that is exactly what it was. Initially it was, literally, a screwdriver. Except instead of touching the screw, the Doctor would point it at a screw, and sonic waves would somehow cause it to turn. Several examples of using the sonic screwdriver as a screwdriver can be found in The War Games (1968). There's an excerpt from this story on Youtube which demonstrates the original sonic screwdriver's operation.
Over time the writers devised new capabilities for the sonic screwdriver, gradually turning it into a sort of all purpose magic wand / deus ex machina. But the original name stuck.