The lunar phases were not all named at once, but at different points in history.

The English terms full moon and new moon go way back, to Old English and perhaps beyond. The others began to be used in English in about the 15th century.

Then the "crescent moon" is named for its shape (but whether it's a "sickle" [Sichel in German] or an "eyebrow" [眉 in Chinese] or something else is arbitrary).

The word crescent being used here isn't arbitrary. It comes from Latin luna crescens, where it meant "waxing moon." The Latin word that became crescent originally meant to get bigger (compare crescendo), to wax. Linking the word crescent to a shape came later because it was being used of the moon. So the term crescent moon doesn't come from its shape; the name of the shape comes from the waxing moon.

All of these terms have histories and reasons for being the way they are. Having diverse sources isn't arbitrariness.

-- 
SuStel
http://trimboli.name