Do our sun and moon have names? We seem to have named every moon orbiting other planets. Why haven't we named our own moon? And for that matter, why doesn't our sun have a name since we name or number stars?
What is a name?
A name is a word, that is reasonably unique, that is used to identify a person or thing. When a child is born there is no word that identifies it, and so its parents have to choose a &quot;name&quot;.  Similarly when a new astronomical object, such as an asteroid, is discovered, it has no word that identifies it and so it is assigned first a number and later a name.
But there is already a word that identifies our sun and moon:  &quot;the Sun&quot; and &quot;the Moon&quot;. There is no need for a new name because they already have a name.  Notice that English (unlike some other languages) gives us a typographical clue that these are names, because the first letter is capitalised.  The Moon is a moon of the Earth and the Earth is a planet orbiting the Sun.
Earth, Moon and Sun are the correct names in English.