Why doesn't Earths Moon Have a name like the other moons in our solar system?

Answer 1

I think it's name is just "The Moon".

Perhaps we are simply parochial about the matter. Our moon is, well, ours. It does have other names. Selene for instance, or Luna.
It does; it is either "The Moon" or "Luna".

However, there's no real need to NAME something if there is only one. The planets have names; even in antiquity, there were five visible planets. Thousands of visible stars have names. But there's no special name for the Sun, or the Moon, because they were (as far as they could tell) unique.
From the dawn of mankind until just a few hundred years ago (which is a very, very long time indeed), the ONLY moon in existence was "the moon." When someone talked about the moon, everyone else knew what they were talking about since it was the only one.

It was just an eyeblink ago (in historical time) that telescopes were invented and we found out there were other moons. By that time "Moon," had become our moon's name and to this date when someone says, "Look at the moon." we still look at our moon rather than some other planet's moon(s). Since for most of us, Moon, still means our moon. For astrologists, I guess they specify by saying, "Earth's moon," so other astrologists know which moon they are speaking about.