The connection of Ilmarë's name to 'starlight' is made explicitly in a note to an early form of the Quenta Silmarillion (in volume V of The History of Middle-earth). That version has some differences from the final form, and not least the fact that Ilmarë was there the daughter of Varda, rather than her handmaid. In that context, the naming of Ilmarë after the starlight of Varda, and the connection of her name to Varda's dwelling of Ilmarin become rather easier to understand.