The simplest explanation, in-universe so to speak, would be that you need a new unique name to see the Childlike Empress, and "Mondenkind" isn't really a word that existed before in the German language (certainly not in common parlance). Even the more correct compound noun "Mondkind" would be unusual. "Monden" ist dative plural, so "Mondenkind" would be "child belonging to the moons" or something, but is more likely to be a stylised form. In German, shoving extra syllables into a word is sometimes used to make words sound more "antique" and courtly. And (speculative) the Childlike Empress does not shine her own light, she projects back the phantasies of children.
The less mundane out of universe answer is that, according to some sources, it is a reference to the novel "Moonchild" by British occultist Aleister Crowley. This is borne out by the fact that among Michael Ende's possessions was, according to the newspaper "Mittelbayerische", an "Äquinox" (now on display in the Ende museum), the seal of Crowley's occult society "Thelemic Golden Dawn", which bears the inscription "Tu was du willst, soll sein das ganze Gesetz", or in the original English, "Do what thou wilt shall be the whole of the Law", which is also the inscription on the Auryin medallion in the Neverending Story.
Like many left wing would be revolutionaries from the 1968 student protest who went into political "inner emigration", Michael Ende believed in any number of strange things (some of them even true, such as climate change), so a reference to occultism isn't perhaps that unusual. However, at least as far as I can recall, the connection was not widely known or discussed at the time of publication (but then I was eight when it was published, so I wouldn't really have been interested in that kind of discussion).