Do our sun and moon have names?
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.