The average human eye has a resolving power of around 1/60th of a degree, meaning that under good conditions it can see objects at distances up to roughly 3500 times the size of the object. The Moon being around 380,000km away, means that under ideal conditions we should be able to see objects around 100km across. 

Astronomical objects acquire their names either via long-standing tradition, or through being named by their discoverers. Of all the satellites of the planets, the Moon has the distinction of being the only one known since the dawn of history, and so has no discoverer as such. It has thus retained its traditional name of ‘the Moon’, befitting its unique status.