The Shire of Crescent Moon, as we know it today, was formed in 1978 by Lord Anam, Lady Galawyn and Lord Renwick, on a crescent moon night.
Galawyn originally attempted to register the name Crescent Moon but there was a Shire in the East Kingdom that already went by that name. They next attempted to register Elenithil which was rejected due to the name coming from Tolken Elvish. Finally they settled on Etoiles de Lune [Stars of the Moon] as an alternate.
In the late 1980s, there was discussion of changing the name to something more period sounding (like Carlsby) when the herald, Andreas, saw that the East Kingdom Shire had disbanded and the name Crescent Moon was thus available. It was decided to do a name change as our founders had intended.
And thus we are now known as Crescent Moon. The Shire was originally formed on a night that held a crescent moon. And the three stars represent the three founding members.