The Luna branding was designed by Studio 384 for the launch of Luna. The logo has been with Luna ever since it got announced. The font has changed during that time. Earlier versions of the logo used the Segoe UI Regular fontface and was stylized as "Luna". In a later revision, the logo got stylized as "LUNA" and in the third and current revision, used as of the early Luna Previews, the fontface changed to Segoe UI Semibold.
The Logotype is composed of the moon-mark, and the “Luna” wordmark. The proportional relationship between the two are demonstrated below. The moon-mark dictates the set of proportions for the whole logotype, and the wordmark is half the height of the moon-mark. There is a set safety margin around the logo, that measures half the size of the moon-mark. This is very similar to the way others use metrics to define their logo proportions, like WordPress.